Research Article Estimating the Occurrence of Wind-Driven...

Research ArticleEstimating the Occurrence of Wind-Driven CoastalUpwelling Associated with lsquolsquoAoshiorsquorsquo on the Northeast Shore ofTokyo Bay Japan An Analytical Model

Zhongfan Zhu and Jingshan Yu

College of Water Sciences Beijing Normal University Xinjiekouwai Street 19 Beijing 100875 China

Correspondence should be addressed to Zhongfan Zhu zhuzhongfan1985gmailcom

Received 9 October 2013 Accepted 12 November 2013 Published 20 January 2014

Academic Editors C Dong and F Shi

Copyright copy 2014 Z Zhu and J Yu This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

ldquoAoshiordquo in Tokyo Bay is a hydroenvironmental phenomenon in which seawater appears milky blue due to reflection of sunshineoff surface water which contains lots of sulfur particles Its appearance is due to coastal upwelling of bottom oxygen-depleted waterwhich causes many deaths of shellfish and other aquatic animals around the bay In this study we derived some analytical solutionsin the context of a two-layered fluid and used them to make a simple analytical model to estimate the occurrence of ldquoAoshiordquophenomenon on the northeast shore of Tokyo Bay Comparison with observation data suggested that this model was valid to acertain degree

1 Introduction

At the head of TokyoBay continual blowing of a northeasterlywind often causes coastal upwelling of oxygen-depletedbottom water which leads to many deaths of shellfish andother aquatic animals around the bay During this process alarge amount of hydrogen sulfide originally contained in thebottom water is oxidized to colloidal sulfur particles whenit touches the oxygen in the atmosphere near the surfaceWhen sunshine reflects off surfacewater inwhich these sulfurparticles suspend the color of seawater presents asmilky blueand this phenomenon is termed ldquoAoshiordquo (in Japanese ldquoAordquomeans blue and ldquoShiordquo means tide)

Many researches concerning ldquoAoshiordquo phenomenon [1ndash5]have been done Based on these research results we attemptto carry out the quantitative calculation of this phenomenonespecially wind conditions under which it can appear atthe head of Tokyo Bay In the preliminary study startingfrom governing equations of a two-layered fluid we derivedsome analytical solutions and used them to make a simpleanalytical model to estimate whether ldquoAoshiordquo phenomenoncan happen on the northeast shore of the bay Comparedwith numerical simulation the analytical method adoptedhere can bemore helpful to roughly evaluate wind conditions

under which ldquoAoshiordquo can occur at Tokyo Bay and obtain aqualitative understanding of the factors that can influencethe occurrence of ldquoAoshiordquo although it is based on severalsimplifications and assumptions

The layout of the paper is as follows Section 2 brieflyintroduces engineering background and derivations of ana-lytical solutions Section 3 presents comparison of the ana-lytical model with observational data Section 4 containsconcluding remark and additionally the appendix presentsthe mathematical derivations of the mentioned analyticalsolutions

2 Engineering Background and Derivations ofAnalytical Solutions

21 Engineering Background Facing the PacificOcean Tokyobay (Figure 1(a)) is located in the southeastern part ofHonshuisland of Japan Its main axis length mean width and averagedepth are approximately 60 km 20 km and 15m respectivelyDue to continual blowing of a northeasterly wind coastalupwelling associated with ldquoAoshiordquo phenomenon can beobserved along the coastline from off Funabashi to off Chiba

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 769823 11 pageshttpdxdoiorg1011552014769823

2 The Scientific World Journal

Although actual coastline is complicated we still simplyconsider the research domain to be a rectangular box withthe length of 50 km the width of 20 km and the depth of15m respectively as shown in Figure 1(a) by three solid linesand a dashed line indicating the imaginary southwest shore[6] Dimensions of this chosen domain are illustrated inFigure 1(b) where 119871 denotes the length and the Cartesiancoordinate system is also defined (the origin is in the centerof the domain the 119909 axis follows the northeasterly wind withthe 119910 axis perpendicular to it and the 119911 axis is positive in theupward direction with respect to the still surface level)

Using a two-layered fluid model which is composed ofa well-mixed upper layer and an oxygen-depleted bottomlayer with different densities (these two layers are separatedby a density interface) Zhu and Isobe [6] analyzed the fullprocess of the occurrence of coastal upwelling associatedwith ldquoAoshiordquo When a northeasterly wind suddenly startsto blow uniformly across the static fluid in the domaincoastal upwelling will occur on the northeast shore as longas the wind conditions are enough With the continualpresence of the wind the effect due to the Coriolis forcewill be predominant and coastal upwelling may appear onthe southeast shore The time scale after which the Coriolisforce becomes predominant is empirically considered and itis practicable to consider this time scale to be two days basedon the numerical experiment of coastal upwelling in TokyoBay carried out by Matsuyama et al [1] and the statistics ofldquoAoshiordquo on the southeast shore of the bay Wind conditionsfor the occurrence of upwelling on the southeast shore of thebay have been discussed by Zhu and Isobe [6] and we onlyfocus on upwelling on the northeast shore in this study

For the analysis of upwelling on the northeast shorewe choose a water parcel as indicated by dashed lines inFigure 1(b) and analyze the motion of this water parcel usingthe mentioned two-layered fluid model as schematicallyshown in Figure 1(c) Sudden blowing of a northeasterlywind accelerates this water parcel in the downwind directioncausing the surface level to rise on the southwest shoreand fall on the northeast shore The pressure gradient dueto inequality of the surface level at these two shores willcause the oxygen-depleted water beneath the interface tomove toward the northeast shore until it disappears finallyleading to the tilt of the interface toward the northeastshore If some wind conditions are satisfied the interface willreach the surface level At this point the oxygen-depletedbottom water can touch the oxygen in the atmosphere andldquoAoshiordquo phenomenon will appear on the northeast shore ofthe domain

22 Derivations of Analytical Solutions Starting from gov-erning equations of thementioned two-layeredmodel we canattempt to derive the mathematical expression of wind con-ditions under which upwelling occurs on the northeast shoreSolving directly these governing equations seems difficultand in this study we adopt the followingmethod as presentedin Csanady [7] governing equations can be transformedinto an internal mode and a surface mode for each modegoverning equations can be solved and the solution of any

mentioned parameter should be a simple sum of its solutionin the internal mode and that in the surface mode Allof discussions regarding how these modes are defined andderived in detail can be found in Csanady [7] Compared tothose already introduced we add both terms of interfacialfriction and bottom friction which normally should not beneglected

Governing equations of the internal mode are

120597119880119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

1205971205771015840

119894

120597119909+

ℎ1015840

ℎ + ℎ1015840(120591119908

1205880

minus120591119868119894

120588)

minusℎ

ℎ + ℎ1015840(120591119868119894

1205881015840minus120591119861119894

1205881015840)

(1)

120597119880119894

120597119909=1205971205771015840

119894

120597119905 (2)

and this mode is defined with some relations

119880119894+ 1198801015840

119894= 0 120577

119894= minus120576

ℎ1015840

ℎ + ℎ10158401205771015840

119894 (3)

In these equations (119880119894 1198801015840

119894) are vertically integrated hori-

zontal velocity in the 119909 direction for the upper layer andthe lower one in the internal mode respectively ℎ ℎ1015840 arethicknesses of the upper layer and the lower one respectively120588 1205881015840 are densities of the upper layer and the lower one

respectively 1205880is reference density of water 120577

119894 1205771015840

119894are surface

displacement and interfacial displacement in the internalmode respectively 119892 and 120576 are gravitational acceleration anddensity contrast between two layers (120576 = (120588

1015840minus 120588)120588

1015840) 120591119908

is stress of the northeasterly wind (120591119868119894 120591119861119894) are interfacial

friction and bottom friction in the 119909 direction in the internalmode respectively and 119905 is time

Governing equations of the surface mode are

120597

120597119905(119880119904+ 1198801015840

119904) = minus 119892 (ℎ + ℎ

1015840)120597120577119904

120597119909

+ (120591119908

1205880

minus120591119868119904

120588) + (

120591119868119904

1205881015840minus120591119861119904

1205881015840)

120597

120597119909(119880119904+ 1198801015840

119904) = minus

120597120577119904

120597119905

(4)

and there exists some relations in this mode

119880119904

ℎ=1198801015840

119904

ℎ1015840 120577

1015840

119904=

ℎ1015840

ℎ + ℎ1015840120577119904 (5)

In these equations all of the quantities with the subscriptldquo119904rdquo have same meanings as introduced above but denote theparameters in the surface mode

Interfacial friction term is assumed to be expressed interms of the velocity difference between the upper layer andthe lower one here as

120591119868119894asymp 120588119862119868(119880119894

ℎminus1198801015840

119894

ℎ1015840) = 120588

10158401198621015840

119868(119880119894

ℎminus1198801015840

119894

ℎ1015840)

120591119868119904asymp 120588119862119868(119880119904

ℎminus1198801015840

119904

ℎ1015840) = 120588

10158401198621015840

119868(119880119904

ℎminus1198801015840

119904

ℎ1015840)

(6)

The Scientific World Journal 3

Funabashi

Chiba

Yokohama Tokyo Bay

Japan

Chiba Light Beacon

Edogawarinkai

Ichihara

Honshu

Tokyo Bay

Miura Peninsula

Boso Peninsula

Pacific ocean

Kantō region

Urayasu

MakuhariIchigawa

139∘40998400E 139∘50998400E 140∘00998400E

35∘40998400N

35∘30998400N

35∘20998400N

35∘10998400N

(a)

Northeast

Northeastshore

Southeast shore

Northwest shore

Southwestshore

Northeasterlywind

x

y

z

L

(b)

Northeasterly wind

x

y

z

L

The mixed upper layer

The bottom layer

SouthwestNortheastshoreshore

(c)

Figure 1 (a) Map of Tokyo Bay including the chosen research domain (b) dimensions of the domain (c) schematic diagram of coastalupwelling on the northeast shore caused by the blowing of a northeasterly wind [6]

where 119862119868 1198621015840

119868are interfacial friction coefficients of the upper

layer and the lower one respectively similarly bottomfriction term is assumed to be expressed in terms of thevelocity of the lower layer as

120591119861119894asymp 1205881015840119862119861

1198801015840

119894

ℎ1015840 120591

119861119904asymp 1205881015840119862119861

1198801015840

119904

ℎ1015840 (7)

where 119862119861is bottom friction coefficient

Substituting (6) and (7) into (1) and using (3) can yield

120597119880119894

120597119905+ 1198961119880119894= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

1205971205771015840

119894

120597119909+

ℎ1015840

ℎ + ℎ1015840

120591119908

1205880

(8)

where a new parameter 1198961is defined as 119896

1= 119862119868ℎ + 119862

1015840

119868ℎ1015840+

119862119861ℎ[ℎ1015840(ℎ + ℎ

1015840)] and this parameter expresses the influences

of interfacial friction and bottom friction By virtue of theLaplace-transformmethod analytical solutions to (8) and (2)

subject to boundary conditions that 119880119894(119909 119905) = 0 at 119909 = plusmn1198712

can be obtained as following (a brief derivation can be foundin the appendix)

1205771015840

119894(119909 119905) = minus

1

119892120576ℎ

120591119908

1205880

119909 +1

119892120576ℎ

120591119908

1205880

4119871

1205872119890minus(11989612)119905

times

+infin

sum

119899=1

(minus1)119899minus1 sin ((2119899 minus 1) 120587119909119871)

(2119899 minus 1)2

times((11989612) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(9)

119880119894 (119909 119905) =

4ℎ1015840

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(11989612)119905

times

+infin

sum

119899=1

(minus1)119899minus1 cos ((2119899 minus 1) 120587119909119871)

(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(10)


where a parameter 120590119899

is defined as 120590119899

=

radic1198962

1minus 4119892120576ℎℎ1015840(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2 3 and

this parameter can be regarded as a parameter relatedto the oscillation of surface displacement or interfacialdisplacement in the internal mode With (9) and (10)expressions of other parameters in the internal mode canbe obtained according to (3) The right side of (9) generallyconsists of two terms the first term is independent of time119905 and the other term is a complicated function of time Itcan be inferred that this complicated function approacheszero when the time is infinitely long (119905 rarr infin) implyingthat the first term is a steady-state solution and the otherone expresses the manner in which this steady state isreached All that remain are 119880

119894rarr 0 in (10) and 1198801015840

119894rarr 0

inferred from both of (10) and (3) when time is infinitelylong (119905 rarr infin) meaning that there is a vertical circulation ineach of the upper layer and the lower one at the steady state

Substituting (6) and (7) into (4) and using (5) one canhave

120597119880119904

120597119905+

119862119861

ℎ + ℎ1015840119880119904= minus119892ℎ

120597120577119904

120597119909+

ℎ

ℎ + ℎ1015840

120591119908

1205880

120597119880119904

120597119909= minus

ℎ

ℎ + ℎ1015840

120597120577119904

120597119905

(11)

Similarly solving these equations subject to boundary con-ditions that 119880

119904(119909 119905) = 0 at 119909 = plusmn1198712 by using the Laplace-

transform method one can get

120577119904 (119909 119905) =

1

119892 (ℎ + ℎ1015840)

120591119908

1205880

119909 minus1

119892 (ℎ + ℎ1015840)

120591119908

1205880

4119871

1205872119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(12)

119880119904 (119909 119905) =

4ℎ

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(13)

where a new parameter 120590119899


=

radic[119862119861(ℎ + ℎ1015840)]

2minus 4119892(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2

3 and this parameter can be regarded as a parameterrelated to the oscillation of surface displacement orinterfacial displacement in the surface mode With (12) and(13) expressions of other parameters in the surface modecan be obtained according to (5) Similar to (9) the rightside of (12) is also composed of a steady-state solution andthe term expressing the manner in which this steady stateis approached The vanishing 119880

119904(119909 119905) from (13) and 1198801015840

119904(119909 119905)

which can be inferred from both (13) and (5) when time isinfinitely long (119905 rarr infin) imply the existence of a verticalcirculation in each of the upper and lower layers at the steadystate

Table 1 Typical parameter values for Tokyo Bay

The parameter ValueThickness of the upper layer ℎ 5mThickness of the lower layer ℎ1015840 10mDensity of the upper layer 120588 1020 kgm3

Density of the lower layer 1205881015840 1023 kgm3

Density contrast 120576 293 times 10minus3

Length of the bay 119871 50 kmReference density 120588

01000 kgm3

Air density 120588119886

123 kgm3

Surface drag coefficient 1205742119886

130 times 10minus3

Interfacial friction coefficientof the upper layer 119862

119868

050 times 10minus5ms

Interfacial friction coefficientof the lower layer 1198621015840

119868


Bottom friction coefficient 119862119861


The parameter expressing the influences ofinterfacial friction and bottom friction 119896

1

167 times 10minus6 sminus1

Total expression of surface displacement 120577total(119909 119905) is thesum of the right-hand side of (9) multiplied by the factorminus120576ℎ1015840(ℎ + ℎ

1015840) and the right-hand side of (12) and total

expression of interfacial displacement 1205771015840total(119909 119905) is the sumof the right-hand side of (9) and the right-hand side of (12)multiplied by the factor ℎ1015840(ℎ + ℎ1015840)

When upwelling only occurs on the northeast shore ata time 119905 = 119879 (119879 is duration of the northeasterly wind) thesumof absolute values of surface displacement and interfacialdisplacement should simply be equal to the thickness of theupper layer (|120577total(minus1198712 119879)|+120577

1015840

total(minus1198712 119879) = ℎ) and a windstress can be gotten Consider120591119908

1205880

= ℎ times 4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

]

+4119871

1198921205872

ℎ

(ℎ + ℎ1015840)2

times [1205872

8minus 119890minus(1198621198612(ℎ+ℎ

1015840))119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119879+120590119899cosh120590

119899119879)

120590119899

]

minus1


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 510

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Eq (14)

Y

N

T = 2days

Figure 2 Presentation of the analytical model using typical parameter values in in Table 1

Table 2 Algebraically averaged thickness value of the upper well-mixed layer for each month calculated based on real-time data taken from2003 to 2010

May Jun Jul Aug Sep Oct NovThe thickness of the upper well-mixed layer (m) 488 463 400 406 313 363 488The thickness of the lower layer (m) 1013 1038 1100 1094 1188 1138 1013

asymp ℎ(4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

asymp 119892120576ℎ21205872

times (4119871[1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

(14)

In this expression the reason why the first approximateequality exists is that the term 4119871(119892ℎ1205872)[1120576 + ℎ1015840(ℎ + ℎ1015840)] ismuch larger than the term 4119871ℎ[1198921205872(ℎ + ℎ1015840)2] in the denom-inator term implying that the contribution of the surfacemode to surface displacement or interfacial displacement canbe negligible compared with the internal mode The reason

why the second approximate equality exists is that the term1120576 is much larger than the term ℎ

1015840(ℎ + ℎ

1015840) meaning

that surface displacement can be neglected compared withinterfacial displacement Furthermore it can be inferred thatif wind duration 119879 is fixed increasing 120591

1199081205880yields larger

values for |120577total(minus1198712 119879)| and 1205771015840

total(minus1198712 119879) This means that(14) actually represents the minimum wind stress for theoccurrence of coastal upwelling associated with ldquoAoshiordquo onthe northeast shore of the domain In addition (14) can beexpressed to be1198921015840ℎ2(1199062

lowast119871) asymp 12minus4120587

2times119890minus11989611198792sum+infin

119899=11(2119899minus

1)2(1198961sinh120590

1198991198792 + 120590

119899cosh120590

119899119879)120590119899 where 1198921015840 is the reduced

gravitational acceleration (1198921015840 = 119892120576) and 119906lowastis the shear

velocity of the surface-wind stress at the fluid side (119906lowast=

radic1205911199081205880) The term 119892

1015840ℎ2(1199062

lowast119871) has been termed as the

Wedderburn number (eg Shintani et al [8]) and it consistsof the Richardson number and the aspect ratio of the domainℎ119871

3 Comparison with Observation Data

31 Presentation of the Model The term of the wind stress in(14) can be expressed to be a quadratic function of wind speed[1]

120591119908= 1205881198861205742

1198861199082 (15)

where 120588119886is the air density 1205742

119886is the surface drag coefficient

and 119908 is average wind speed which is measured 10m abovethe still surface


In order to present (14) we assign some empirical valuesto unknown parameters in this equation as presented inTable 1 also including known parameters In this table asimple estimate for 119862

119868 119862119861shows that they should be on the

order of 10minus6ndash10minus5 so we have chosen the empirical value 050times 10minus5 Values for densities and thicknesses of the upper layerand the lower one are only adopted as an example and theyoriginate from the numerical experiment of Matsuyamaet al[1] where they are representative of the typical stratificationof Tokyo Bay in summer

Equation (14) is presented in Figure 2 and in this figurethe combination of (14) and the line 119879 = 2 days divides theentire region into two different regions RegionY is the regioninwhich upwelling can occur on the northeast shore of Tokyobay and region N is the region without upwelling on thisshore If the wind speed and the wind duration are knownit is possible to estimate whether upwelling associated withldquoAoshiordquo can appear on the northeast shore of the bay usingthis figure

32 Treatment of Observation Data Observation data ofldquoAoshiordquo in Tokyo Bay from 1978 to 2010 are availableand they originate from three different sources [6] Amongthese we selected data sets of ldquoAoshiordquo only observed onthe northeast shore We adopted data sets of wind measuredat Edogawarinkai station which is indicated in Figure 1(a)and further calculated average speed and total durationof the northeasterly-oriented wind that contributes to theoccurrence of ldquoAoshiordquo [6] For all of the real cases in whichldquoAoshiordquo appeared on the northeast shore all of the parametervalues can be treated as constants as presented in Table 1except for the thickness of the upper well-mixed layer ℎ andthe density contrast 120576 This is because these two parametersare closely related to the degree of stratification and theyshould be different from one case to another In order tocalculate them for each case we used real-time datameasuredat the Chiba Light Beacon (CLB) also indicated in Figure 1(a)[6] The thickness of the well-mixed upper layer can beestimated from vertical distribution contours of temperaturesalinity and dissolved oxygen and the densities of the upperand lower layers can be calculated based on the temperatureand the salinity However these data sets provided at CLBonly range from 2003 to 2010 For those real cases from 1978to 2002 that lack real-time data we adopted the followingstrategy as presented in Zhu and Isobe [6] we focused onthe seasonal variation of stratification and considered thealgebraically averaged thickness values and density valuesfor each month from 2003 to 2010 to be representative ofreal cases observed from 1978 to 2002 Calculated monthly-mean densities and algebraically averaged densities of theupper layer and the lower one for each month have beenprovided in Zhu and Isobe [6] and monthly-mean thicknessand algebraically averaged thickness of the upper well-mixedlayer are shown in Figure 3 and Table 2 respectively Inaddition it needs to be stated that this study did not use thespatial averaged wind data and stratification data in TokyoBay because of a lack of long-term real-time data measuredat different locations in the bay beyond CLB

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar15

2

25

3

35

4

45

5

55

6

65

Month

h (m

)

The thickness of the upper well-mixed layer

2003200420052006

2007200820092010

Figure 3 Monthly-mean thickness value of the upper well-mixedlayer from 2003 to 2010

33 Comparison Result Table 3 summarizes the comparisonresult of the model with real cases of ldquoAoshiordquo observed onthe northeast shore of Tokyo Bay from 2003 to 2010 Thefirst column shows occurrence date and occurrence area ofldquoAoshiordquo (In ldquoOccurrence areardquo column the expression ldquoA-Brdquo denotes the area which ranges from A to B hereafter)The second column presents the calculated average windspeed in the northeast-southwest direction and the windduration The third column show the degree of stratificationusing measurement data from CLB Using these values thefourth column presents the calculated model Conclusionsabout whether each of real cases is in accord with the modelare shown in the fifth column suggesting that one of threereal cases agrees with the proposed model Figures 4(a)ndash4(g)shows the comparison result of themodelwith real cases from1978 to 2002 using the representative values of each monthFrom these figures it can be found that almost sixty-threepercent of real cases are consistent with the model As anaddition Table 4 presents occurrence dates and occurrenceareas of these real cases as well as wind conditions Amongall of real cases which did not agree with the model it can befound that the duration of the northeasterly-oriented windexceeds two days in nine real cases (as presented in thelast row of Table 3 and Figures 4(d)ndash4(g)) for which theeffect due to the Coriolis force cannot be simply negligibleWe compared them with the criteria proposed by Zhu andIsobe [6] for the occurrence of ldquoAoshiordquo on the southeastshore of the bay as presented in the last column in Table 3and the third column of Table 4 and further found thatldquoAoshiordquo can happen on the southeast shore in all of thesecases The appearance of the phenomenon that ldquoAoshiordquo areawas not on the southeast shore but on the northeast shore


Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)

Figure 4 Comparison of the model with real cases of Aoshio observed from 1978 to 2002 in a particular month (a) May (b) June (c) July(d) August (e) September (f) October and (g) November

may be due to the anticlockwise movement of ldquoAoshiordquo areafrom the southeast shore to the northeast shore under theinfluence of the propagation of internal Kelvin waves afterthe cessation of the northeasterly wind as clearly presentedin the numerical simulation of Matsuyama et al [1] andfurther pointed out in Ueno et al [4] and Nakatsujiet al[5] More analyses about the role that internal Kelvin wavesplay in the movement of ldquoAoshiordquo area were not mentionedin this study and will be performed in future research Therelated discussions for those real cases which neither satisfythe criteria for ldquoAoshiordquo on the southeast shore nor agree withthe analytical model (they are cases of that ldquoAoshiordquo occurredin June 13 1979 August 24 1984 June 1 and July 2 1992and May 16 2005) were not carried out in this preliminarystudy because of a lack of the detailed observation dataregarding these cases (especially the detailed descriptionsof the movement of the oxygen-depleted bottom water inthese cases) In conclusion considering that several simpli-fications and assumptions were used it can be suggestedthat the analytical model proposed here is valid to a certaindegree

4 Concluding Remarks

In this study we have derived some analytical solutions inthe context of a two-layered fluid and have used them tomake a simple analytical model to estimate the occurrenceof ldquoAoshiordquo phenomenon on the northeast shore of TokyoBay Comparison with observational data suggested that thismodel was valid to a certain degree

Appendix

Taking the derivative of (2) with respect to 119905 and thederivative of (8) with respect to 119909 respectively and combingthem can yield

12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)

Introducing the Laplace transform of a arbitrary function120593(119905) as 119876(120593) = int

infin

0119890minus119904119905120593(119905)119889119905 (119904 is a parameter in the

transformation) (A1) can be transformed to be

119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)

The analytical solution of this equation complying withthe boundary conditions is

119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)


Table 4 Occurrence dates occurrence areas and wind conditions of real cases of Aoshio observed on the northeast shore of Tokyo Bay from1978 to 2002

Upwelling associated with Aoshioon the northeast shore of Tokyo Bay

Northeasterlywind

Does the real case satisfythe criteria for Aoshio onthe southeast shoreproposed byZhu and Isobe (2012) [6]

Occurrence date Occurrence areaAverage Windspeedwind

duration (ms)(h)1978 May 31 Urayasu-Funabashi 37324 mdash

1979Jun 13 Funabashi 33614 mdash

Jul 16-Jul 17 Makuhari 43047 mdashAug 14ndashAug 16 Makuhari 42542 mdash

1980 Aug 2ndashAug 5 Funabashi-Makuhari 58024 mdashSep 19 Funabashi 39641 mdash

1982May 21ndashMay 23 Ichigawa 45544 mdashJul 27ndashJul 29 Ichigawa-Makuhari 35047 mdash

Sep 6 Funabashi 503133 Yes


1985 Jun 15ndashJun 18 Funabashi 60748 mdash1986 Aug 4 Urayasu-Ichigawa 39458 Yes

1988 May 24 Funabashi 49448 mdashSep 3ndashSep 8 Funabashi 37524 mdash

1989

Jun 20 Funabashi 42848 mdashAug 26-Aug 27 Funabashi 45024 mdashSep 22ndashSep 24 Funabashi-Makuhari 39245 mdash

Oct 30 Funabashi-Makuhari 33575 Yes

1990

Jun 28ndashJul 2 Funabashi-Makuhari 41824 mdash

Aug 6 Ichigawa-Funabashi-Makuhari 58948 mdash

Sep 7-Sep 8 Urayasu-Funabashi 47224 mdashSep 27ndashSep 29 Funabashi-Makuhari 39938 mdash

1992Jun 1 Funabashi-Makuhari 28022 mdashJul 2 Funabashi 41813 mdash

Aug 3ndashAug 6 Ichigawa-Funabashi 51243 mdash1994 Nov 4ndashNov 8 Makuhari-Funabashi 345107 Yes1996 Sep 10ndashSep 12 Funabashi-Makuhari 37123 mdash

1999 Sep 30 Funabashi 29762 YesOct 18ndashOct 20 Funabashi 34687 Yes

2000 Sep 27ndashSep 29 Funabashi 28562 Yes

2001 Apr 23-Apr 24 Funabashi 43924 mdash

Oct 9-Oct 10Makuhari andFunabashi and

Ichigawa399116 Yes

To invert this Laplace transform we define such a func-tion 119891(119909 119905) so that

119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)

This function is analytic everywhere except at a series ofpoles 119904 = 0 119904 = minus119896

1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)

The residues at 119904 = 0 and 119904 = minus1198961are zero


The residues at 119904 = minus11989612 + 120590

119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be

Residues at 119904 = minus11989612plusmn 120590119899

=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)

sin ((2119899 minus 1) 120587119909119871)sin (119899 minus 12) 120587

times [119890(minus11989612+120590119899)119905minus 119890(minus11989612minus120590119899)119905]

(A6)

which gives the expression of the stated function 119891(119909 119905) byusing the residue theorem Using the convolution theoremthe function 1205771015840

119894(119909 119905) in (A3) can be gained (it can be found

that 119876(1) = 1119904 in this equation) The function 119880119894(119909 119905) can

also be obtained by combining (2)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The first author would like to express the deepest gratitudeto Professor Emeritus Masahiko Isobe in the Universityof Tokyo in Japan for his careful guidance during thedoctoral study Special thanks are due to three reviewersfor their valuable comments This research is supported bythe National Key Technology Research and DevelopmentProgram of the Ministry of Science and Technology of China(no 2013BAB05B04) This research is also supported by ldquotheFundamental Research Funds for the Central Universitiesrdquo inChina (no 2013NT50)

References

[1] M Matsuyama K Touma and A Ohwaki ldquoNumerical exper-iments of upwelling in Tokyo Bay in relation to ldquoAoshiordquo (theupwelled anoxic blue-green turbid water)rdquo Bulletin on CoastalOceanography vol 28 pp 63ndash74 1990 (Japanese)

[2] K Otsubo A Harashima T Miyazaki Y Yasuoka and KMuraoka ldquoField survey and hydraulic study of ldquoAoshiordquo inTokyo BayrdquoMarine Pollution Bulletin vol 23 pp 51ndash55 1991

[3] K Nakatsuji S Nagasaka and K Muraoka ldquoBasic experimentson upwelling of anoxic water lsquoAoshiorsquo observed in Tokyo BayJapanrdquo in Proceedings of Hydraulic Engineering vol 35 pp603ndash608 Japan Society of Civil Engineers Tokyo Japan 1991(Japanese)

[4] S Ueno K Nadaoka A Ishimura and H Katsui ldquoAnalysison the upwelling due to wind in Tokyo Bay based on NOAA-AVHRR datardquo in Proceedings of Coastal Engineering vol 39pp 256ndash260 Japan Society of Civil Engineers Tokyo 1992(Japanese)

[5] K Nakatsuji J S Yoon T Yuasa and K Muraoka ldquoThe rela-tionship between wind-driven stratified flow and occurrencemechanism of blue tiderdquo in Proceedings of Coastal Engineeringvol 42 pp 1066ndash1070 Japan Society of Civil Engineers TokyoJapan 1995

[6] Z Zhu and M Isobe ldquoCriteria for the occurrence of wind-driven coastal upwelling associated with ldquoAoshiordquo on the south-east shore of Tokyo Bayrdquo Journal of Oceanography vol 68 pp561ndash574 2012

[7] G T Csanady Circulation in the Coastal Ocean D ReidelDordrecht The Netherlands 1982

[8] T Shintani A de la Fuente Y Nino and J Imberger ldquoGeneral-izations of the wedderburn number parameterizing upwellingin stratified lakesrdquo Limnology and Oceanography vol 55 no 3pp 1377ndash1389 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of


EarthquakesJournal of


Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining


Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of


Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering


GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of


OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in


MineralogyInternational Journal of


MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Geological ResearchJournal of


Geology Advances in


Although actual coastline is complicated we still simplyconsider the research domain to be a rectangular box withthe length of 50 km the width of 20 km and the depth of15m respectively as shown in Figure 1(a) by three solid linesand a dashed line indicating the imaginary southwest shore[6] Dimensions of this chosen domain are illustrated inFigure 1(b) where 119871 denotes the length and the Cartesiancoordinate system is also defined (the origin is in the centerof the domain the 119909 axis follows the northeasterly wind withthe 119910 axis perpendicular to it and the 119911 axis is positive in theupward direction with respect to the still surface level)

Using a two-layered fluid model which is composed ofa well-mixed upper layer and an oxygen-depleted bottomlayer with different densities (these two layers are separatedby a density interface) Zhu and Isobe [6] analyzed the fullprocess of the occurrence of coastal upwelling associatedwith ldquoAoshiordquo When a northeasterly wind suddenly startsto blow uniformly across the static fluid in the domaincoastal upwelling will occur on the northeast shore as longas the wind conditions are enough With the continualpresence of the wind the effect due to the Coriolis forcewill be predominant and coastal upwelling may appear onthe southeast shore The time scale after which the Coriolisforce becomes predominant is empirically considered and itis practicable to consider this time scale to be two days basedon the numerical experiment of coastal upwelling in TokyoBay carried out by Matsuyama et al [1] and the statistics ofldquoAoshiordquo on the southeast shore of the bay Wind conditionsfor the occurrence of upwelling on the southeast shore of thebay have been discussed by Zhu and Isobe [6] and we onlyfocus on upwelling on the northeast shore in this study

For the analysis of upwelling on the northeast shorewe choose a water parcel as indicated by dashed lines inFigure 1(b) and analyze the motion of this water parcel usingthe mentioned two-layered fluid model as schematicallyshown in Figure 1(c) Sudden blowing of a northeasterlywind accelerates this water parcel in the downwind directioncausing the surface level to rise on the southwest shoreand fall on the northeast shore The pressure gradient dueto inequality of the surface level at these two shores willcause the oxygen-depleted water beneath the interface tomove toward the northeast shore until it disappears finallyleading to the tilt of the interface toward the northeastshore If some wind conditions are satisfied the interface willreach the surface level At this point the oxygen-depletedbottom water can touch the oxygen in the atmosphere andldquoAoshiordquo phenomenon will appear on the northeast shore ofthe domain

22 Derivations of Analytical Solutions Starting from gov-erning equations of thementioned two-layeredmodel we canattempt to derive the mathematical expression of wind con-ditions under which upwelling occurs on the northeast shoreSolving directly these governing equations seems difficultand in this study we adopt the followingmethod as presentedin Csanady [7] governing equations can be transformedinto an internal mode and a surface mode for each modegoverning equations can be solved and the solution of any

mentioned parameter should be a simple sum of its solutionin the internal mode and that in the surface mode Allof discussions regarding how these modes are defined andderived in detail can be found in Csanady [7] Compared tothose already introduced we add both terms of interfacialfriction and bottom friction which normally should not beneglected

Governing equations of the internal mode are

120597119880119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

1205971205771015840

119894

120597119909+

ℎ1015840

ℎ + ℎ1015840(120591119908

1205880

minus120591119868119894

120588)

minusℎ

ℎ + ℎ1015840(120591119868119894

1205881015840minus120591119861119894

1205881015840)

(1)

120597119880119894

120597119909=1205971205771015840

119894

120597119905 (2)

and this mode is defined with some relations

119880119894+ 1198801015840

119894= 0 120577

119894= minus120576

ℎ1015840

ℎ + ℎ10158401205771015840

119894 (3)

In these equations (119880119894 1198801015840

119894) are vertically integrated hori-

zontal velocity in the 119909 direction for the upper layer andthe lower one in the internal mode respectively ℎ ℎ1015840 arethicknesses of the upper layer and the lower one respectively120588 1205881015840 are densities of the upper layer and the lower one

respectively 1205880is reference density of water 120577

119894 1205771015840

119894are surface

displacement and interfacial displacement in the internalmode respectively 119892 and 120576 are gravitational acceleration anddensity contrast between two layers (120576 = (120588

1015840minus 120588)120588

1015840) 120591119908

is stress of the northeasterly wind (120591119868119894 120591119861119894) are interfacial

friction and bottom friction in the 119909 direction in the internalmode respectively and 119905 is time

Governing equations of the surface mode are

120597

120597119905(119880119904+ 1198801015840

119904) = minus 119892 (ℎ + ℎ

1015840)120597120577119904

120597119909

+ (120591119908

1205880

minus120591119868119904

120588) + (

120591119868119904

1205881015840minus120591119861119904

1205881015840)

120597

120597119909(119880119904+ 1198801015840

119904) = minus

120597120577119904

120597119905

(4)

and there exists some relations in this mode

119880119904

ℎ=1198801015840

119904

ℎ1015840 120577

1015840

119904=

ℎ1015840

ℎ + ℎ1015840120577119904 (5)

In these equations all of the quantities with the subscriptldquo119904rdquo have same meanings as introduced above but denote theparameters in the surface mode

Interfacial friction term is assumed to be expressed interms of the velocity difference between the upper layer andthe lower one here as

120591119868119894asymp 120588119862119868(119880119894

ℎminus1198801015840

119894

ℎ1015840) = 120588

10158401198621015840

119868(119880119894

ℎminus1198801015840

119894

ℎ1015840)

120591119868119904asymp 120588119862119868(119880119904

ℎminus1198801015840

119904

ℎ1015840) = 120588

10158401198621015840

119868(119880119904

ℎminus1198801015840

119904

ℎ1015840)

(6)


Funabashi

Chiba

Yokohama Tokyo Bay

Japan

Chiba Light Beacon

Edogawarinkai

Ichihara

Honshu

Tokyo Bay

Miura Peninsula

Boso Peninsula

Pacific ocean

Kantō region

Urayasu

MakuhariIchigawa

139∘40998400E 139∘50998400E 140∘00998400E

35∘40998400N

35∘30998400N

35∘20998400N

35∘10998400N

(a)

Northeast

Northeastshore

Southeast shore

Northwest shore

Southwestshore

Northeasterlywind

x

y

z

L

(b)

Northeasterly wind

x

y

z

L


The bottom layer


(c)


where 119862119868 1198621015840



120591119861119894asymp 1205881015840119862119861

1198801015840

119894

ℎ1015840 120591

119861119904asymp 1205881015840119862119861

1198801015840

119904

ℎ1015840 (7)



120597119880119894

120597119905+ 1198961119880119894= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

1205971205771015840

119894

120597119909+

ℎ1015840

ℎ + ℎ1015840

120591119908

1205880

(8)


1= 119862119868ℎ + 119862

1015840

119868ℎ1015840+

119862119861ℎ[ℎ1015840(ℎ + ℎ





1205771015840

119894(119909 119905) = minus

1

119892120576ℎ

120591119908

1205880

119909 +1

119892120576ℎ

120591119908

1205880

4119871

1205872119890minus(11989612)119905

times

+infin

sum

119899=1


(2119899 minus 1)2

times((11989612) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(9)

119880119894 (119909 119905) =

4ℎ1015840

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(11989612)119905

times

+infin

sum

119899=1


(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(10)




=

radic1198962

1minus 4119892120576ℎℎ1015840(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2 3 and


119894rarr 0 in (10) and 1198801015840

119894rarr 0



120597119880119904

120597119905+

119862119861

ℎ + ℎ1015840119880119904= minus119892ℎ

120597120577119904

120597119909+

ℎ

ℎ + ℎ1015840

120591119908

1205880

120597119880119904

120597119909= minus

ℎ

ℎ + ℎ1015840

120597120577119904

120597119905

(11)




120577119904 (119909 119905) =

1

119892 (ℎ + ℎ1015840)

120591119908

1205880

119909 minus1

119892 (ℎ + ℎ1015840)

120591119908

1205880

4119871

1205872119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(12)

119880119904 (119909 119905) =

4ℎ

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(13)



=

radic[119862119861(ℎ + ℎ1015840)]

2minus 4119892(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2


119904(119909 119905) from (13) and 1198801015840

119904(119909 119905)







01000 kgm3


123 kgm3


130 times 10minus3


119868



119868





1






1015840


1205880

= ℎ times 4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

]

+4119871

1198921205872

ℎ

(ℎ + ℎ1015840)2

times [1205872

8minus 119890minus(1198621198612(ℎ+ℎ

1015840))119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119879+120590119899cosh120590

119899119879)

120590119899

]

minus1


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 510

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Eq (14)

Y

N

T = 2days




asymp ℎ(4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

asymp 119892120576ℎ21205872

times (4119871[1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

(14)



1015840(ℎ + ℎ

1015840) meaning







119899=11(2119899minus

1)2(1198961sinh120590

1198991198792 + 120590

119899cosh120590




radic1205911199081205880) The term 119892

1015840ℎ2(1199062





120591119908= 1205881198861205742

1198861199082 (15)











2

25

3

35

4

45

5

55

6

65

Month

h (m

)


2003200420052006

2007200820092010




Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Funabashi

Chiba

Yokohama Tokyo Bay

Japan

Chiba Light Beacon

Edogawarinkai

Ichihara

Honshu

Tokyo Bay

Miura Peninsula

Boso Peninsula

Pacific ocean

Kantō region

Urayasu

MakuhariIchigawa

139∘40998400E 139∘50998400E 140∘00998400E

35∘40998400N

35∘30998400N

35∘20998400N

35∘10998400N

(a)

Northeast

Northeastshore

Southeast shore

Northwest shore

Southwestshore

Northeasterlywind

x

y

z

L

(b)

Northeasterly wind

x

y

z

L


The bottom layer


(c)


where 119862119868 1198621015840



120591119861119894asymp 1205881015840119862119861

1198801015840

119894

ℎ1015840 120591

119861119904asymp 1205881015840119862119861

1198801015840

119904

ℎ1015840 (7)



120597119880119894

120597119905+ 1198961119880119894= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

1205971205771015840

119894

120597119909+

ℎ1015840

ℎ + ℎ1015840

120591119908

1205880

(8)


1= 119862119868ℎ + 119862

1015840

119868ℎ1015840+

119862119861ℎ[ℎ1015840(ℎ + ℎ





1205771015840

119894(119909 119905) = minus

1

119892120576ℎ

120591119908

1205880

119909 +1

119892120576ℎ

120591119908

1205880

4119871

1205872119890minus(11989612)119905

times

+infin

sum

119899=1


(2119899 minus 1)2

times((11989612) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(9)

119880119894 (119909 119905) =

4ℎ1015840

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(11989612)119905

times

+infin

sum

119899=1


(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(10)




=

radic1198962

1minus 4119892120576ℎℎ1015840(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2 3 and


119894rarr 0 in (10) and 1198801015840

119894rarr 0



120597119880119904

120597119905+

119862119861

ℎ + ℎ1015840119880119904= minus119892ℎ

120597120577119904

120597119909+

ℎ

ℎ + ℎ1015840

120591119908

1205880

120597119880119904

120597119909= minus

ℎ

ℎ + ℎ1015840

120597120577119904

120597119905

(11)




120577119904 (119909 119905) =

1

119892 (ℎ + ℎ1015840)

120591119908

1205880

119909 minus1

119892 (ℎ + ℎ1015840)

120591119908

1205880

4119871

1205872119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(12)

119880119904 (119909 119905) =

4ℎ

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(13)



=

radic[119862119861(ℎ + ℎ1015840)]

2minus 4119892(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2


119904(119909 119905) from (13) and 1198801015840

119904(119909 119905)







01000 kgm3


123 kgm3


130 times 10minus3


119868



119868





1






1015840


1205880

= ℎ times 4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

]

+4119871

1198921205872

ℎ

(ℎ + ℎ1015840)2

times [1205872

8minus 119890minus(1198621198612(ℎ+ℎ

1015840))119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119879+120590119899cosh120590

119899119879)

120590119899

]

minus1


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 510

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Eq (14)

Y

N

T = 2days




asymp ℎ(4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

asymp 119892120576ℎ21205872

times (4119871[1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

(14)



1015840(ℎ + ℎ

1015840) meaning







119899=11(2119899minus

1)2(1198961sinh120590

1198991198792 + 120590

119899cosh120590




radic1205911199081205880) The term 119892

1015840ℎ2(1199062





120591119908= 1205881198861205742

1198861199082 (15)











2

25

3

35

4

45

5

55

6

65

Month

h (m

)


2003200420052006

2007200820092010




Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




=

radic1198962

1minus 4119892120576ℎℎ1015840(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2 3 and


119894rarr 0 in (10) and 1198801015840

119894rarr 0



120597119880119904

120597119905+

119862119861

ℎ + ℎ1015840119880119904= minus119892ℎ

120597120577119904

120597119909+

ℎ

ℎ + ℎ1015840

120591119908

1205880

120597119880119904

120597119909= minus

ℎ

ℎ + ℎ1015840

120597120577119904

120597119905

(11)




120577119904 (119909 119905) =

1

119892 (ℎ + ℎ1015840)

120591119908

1205880

119909 minus1

119892 (ℎ + ℎ1015840)

120591119908

1205880

4119871

1205872119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119905 + 120590119899cosh120590

119899119905)

120590119899

(12)

119880119904 (119909 119905) =

4ℎ

(ℎ + ℎ1015840)

120591119908

1205880

119890minus(1198621198612(ℎ+ℎ

1015840))119905

times

+infin

sum

119899=1


(2119899 minus 1) 120587

sinh120590119899119905

120590119899

(13)



=

radic[119862119861(ℎ + ℎ1015840)]

2minus 4119892(ℎ + ℎ1015840)(2119899 minus 1)

2120587211987122 119899 = 1 2


119904(119909 119905) from (13) and 1198801015840

119904(119909 119905)







01000 kgm3


123 kgm3


130 times 10minus3


119868



119868





1






1015840


1205880

= ℎ times 4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

]

+4119871

1198921205872

ℎ

(ℎ + ℎ1015840)2

times [1205872

8minus 119890minus(1198621198612(ℎ+ℎ

1015840))119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times

((1198621198612 (ℎ + ℎ

1015840)) sinh120590

119899119879+120590119899cosh120590

119899119879)

120590119899

]

minus1


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 510

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Eq (14)

Y

N

T = 2days




asymp ℎ(4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

asymp 119892120576ℎ21205872

times (4119871[1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

(14)



1015840(ℎ + ℎ

1015840) meaning







119899=11(2119899minus

1)2(1198961sinh120590

1198991198792 + 120590

119899cosh120590




radic1205911199081205880) The term 119892

1015840ℎ2(1199062





120591119908= 1205881198861205742

1198861199082 (15)











2

25

3

35

4

45

5

55

6

65

Month

h (m

)


2003200420052006

2007200820092010




Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 510

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Eq (14)

Y

N

T = 2days




asymp ℎ(4119871

119892ℎ1205872(1

120576+

ℎ1015840

ℎ + ℎ1015840)

times [1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

asymp 119892120576ℎ21205872

times (4119871[1205872

8minus 119890minus(11989612)119879

times

+infin

sum

119899=1

1

(2119899 minus 1)2

times((11989612) sinh120590

119899119879 + 120590119899cosh120590

119899119879)

120590119899

])

minus1

(14)



1015840(ℎ + ℎ

1015840) meaning







119899=11(2119899minus

1)2(1198961sinh120590

1198991198792 + 120590

119899cosh120590




radic1205911199081205880) The term 119892

1015840ℎ2(1199062





120591119908= 1205881198861205742

1198861199082 (15)











2

25

3

35

4

45

5

55

6

65

Month

h (m

)


2003200420052006

2007200820092010




Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in








2

25

3

35

4

45

5

55

6

65

Month

h (m

)


2003200420052006

2007200820092010




Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Table3Com

paris

onof

them

odelwith

realcaseso

fAoshioob

served

onthen

ortheastshoreo

fTokyo

Bayfro

m2003

to2010

(based

onmeasureddatafro

mCh

ibaL

ight

Beacon

)Upw

ellin

gassociated

with

Aoshio

onthen

ortheastshoreo

fTokyo

Bay

Northeaste

rlywind

Degreeo

fstratificatio

nCa

lculated

mod

elprop

osed

inthis

study

Doesthe

realcase

satisfy

thec

alculated

mod

el

Doesthe

realcase

satisfy

thec

riteriafor

Aoshio

onthes

outheastshore

prop

osed

byZh

uand

Isob

e(2012)[6]

Occurrenced

ate

Occurrencea

rea

Averagew

ind

speedwind

duratio

n(m

s)(h)

Surfa

cetemperature

surface

salin

ity(∘C)

(psu)

Botto

mtemperature

bottom

salin

ity(∘C)

(psu)

Densityof

theu

pper

layer

(kgm

3 )

Densityof

thelow

erlayer

(kgm

3 )

The

thickn

esso

ftheu

pper

layer(m)

The

thickn

esso

fthelow

erlayer(m)

2005

May

16-M

ay17

Urayasu-Ic

higawa-

Funabashi

29918

156322

156334

102371

102463

500

1000

119879le2days

1199082ge127311m

2 s2

No

mdash

2007

Oct1-O

ct2

Funabashi

37648

21629

216328

101980

102269

500

1000

119879le2days

1199082ge97

013m

2 s2

Yes

mdash

2008

Nov13-Nov14

Funabashi-Ichigaw

a33895

18322

1923300

102316

102347

500

1000

119879le2daysmdash

No

Yes


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(a)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(b)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(c)

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

02468

1012141618202224

T (hour)

w (m

s)

Y

N

(d)

0 10 20 30 40 50 60 70 80 90 100

110

120

130

1400

2468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(e)

0 10 20 30 40 50 60 70 80 90 100

110

120

02468

1012141618202224

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(f)

Figure 4 Continued


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0 10 20 30 40 50 60 70 80 90 100

110

120

0

2

4

6

8

10

12

14

16

18

20

22

24

T (hour)

w (m

s)

Y

N

Eq (14)

Real casesT = 2days

(g)





Appendix


12059721205771015840

119894

1205971199052+ 1198961

1205971205771015840

119894

120597119905= 119892120576

ℎℎ1015840

ℎ + ℎ1015840

12059721205771015840

119894

1205971199092 (A1)


infin



119892120576ℎℎ1015840

ℎ + ℎ1015840

1198892119876(1205771015840

119894)

1198891199092minus (1199042+ 1198961119904)119876 (120577

1015840

119894) = 0 (A2)


119876(1205771015840

119894) = minus

1

119892120576ℎ

120591119908

1205880

1

119904

times1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A3)




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




Northeasterlywind












1989



1990










Ichigawa399116 Yes


119876 (119891 (119909 119905)) =1

radic(1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840

times

sinh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840)119909]

cosh [radic((1199042 + 1198961119904) (ℎ + ℎ1015840) 119892120576ℎℎ1015840) (1198712)]

(A4)


1 and 119904 = minus119896

12 plusmn 120590

119899 where

120590119899=

radic1198962

1minus 4119892120576ℎℎ1015840 (ℎ + ℎ1015840) (2119899 minus 1)

212058721198712

2

119899 = 1 2 3

(A5)




119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in



119899and 119904 = minus119896

12 minus 120590

119899may be

combined to be


=2119892120576ℎℎ

1015840

120590119899119871 (ℎ + ℎ1015840)



(A6)







Acknowledgments


References


















Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in










Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

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