analiza circulatiei geostrofice. cap 3.doc

8/16/2019 analiza circulatiei geostrofice. cap 3.doc

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Ocean current variability in

relation to o shore engineering.

A thesis submitted in partial fulfillment of therequirements for the degree of

doktor ingeniør

by

Rune Yttervik

Trondheim, !!"

Department of Marine TechnologyFaculty of Engineering Science and Technology Norwegian

University of Science and Technology


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Ackno#ledgements

This #ork #as carried out at the $epartment of %arine Technology at the &or'#egian (niversity of )cience and Technology *&T&(+, under the supervisionof rofessor -arl %artin arsen at &T&( and rofessor // 0unnar 1. 2urnes atthe (niversity in 3ergen *(i3+. Their professional e4pertise, advice andcontributions during the course of this #ork, as #ell as their positive attitude ingeneral, are greatfully ackno#ledged.

Thanks are due to asse ønseth of O-5A&OR and to the Ormen ange

-onsor'tium through &orsk 6ydro A)A, #ho made the current data presentedin chapter 7 available. %agnar Reistad at the 3ergen branch of the &or#egian%eteorological /nstitute provided the hindcastdata for #ind, used in that samechapter8 a service for #hich / am very grateful.

/ am also grateful to rofessor 9arle 3erntsen at (i3 for providing thenumerical ocean model #hich formed the basis for chapter ". 6is kind andpatient response to my various questions and enquiries is much appreciated.

Thanks to my colleagues at the $epartment of %arine Technology at &T&( and

at %AR/&T51. / #ould also like to e4tend thanks to the sta at the 0eophysical

/nstitute at (i3. / appreciate the e ort they made in making me feel #elcome andin introducing me to a ne# and e4citing field of science during my stay there.

This research #as supported by the &or#egian (niversity of )cience andTech'nology *&T&(+, and by the &or#egian %arine Technology Research/nstitute *%AR/&T51+. %AR/&T51s fle4ible attitude in the final stages of this#ork is appreciated.

i


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ii


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Abstract

This #ork adresses ocean current variability in relation to o shore engineering.

The o shore oil and gas activity has up until recently taken place mainly on the

continental shelves around the #orld. $uring the last fe# years, ho#ever, the in'

dustry has moved past the continental shelf edge and do#n the continental slope

to#ards increasingly deeper #aters. /n deep #ater locations, marine structures

may span large spaces, marine operations may become more complicated and

re'quire longer time for completion and the e ect of the surface #aves is

diminished. Therefore, the spatial and temporal variability of the current ise4pected to be'come more important in design and planning than before.

The flo# of #ater in the oceans of the #orld takes place on a #ide variety of spatial

scales, from the main forms of the global ocean circulation *∼km+, to the

microstructure *∼mm+ of boundary layer turbulence. )imilarly, the temporal vari'ability

is also large. /n one end of the scale #e find variations that take place over several

decades, and in the other end #e find small'scale turbulence *∼seconds+. $i erent

features of the flo# are driven by di erent mechanisms. )everal processes and

properties *stratification:, sloping boundary, -oriolis e ect, friction, internal #aves,

etc.+ interact on the continental slope to create a highly variable flo# en'vironment.

Analysis of a set of observed data that #ere recorded close to the seabed on the

continental slope #est of &or#ay are presented. The data suggest that some strong

and abrupt current events *changes in flo# speed of ∼!." m;s in


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iv

very rapidly *#ithin a fe# minutes+ from do#n'slope to up'slope flo#. The

change in speed during this event #as as high as !.? m;s.

Another data set has been analy@ed in order to illustrate the spatial variation inthe current that can sometimes be found. /t is sho#n that the flo# in the upper layer is virtually decoupled from the flo# in the lo#er layer at a location #est of &or#ay. This is either caused by bottom topography, stratification or both.

6igh variability of the current presents ne# requirements to the #ay that thecur'rent should be modelled by the o shore engineer. 2or instance, it isnecessary to consider #hich type of operation;structure that is to be carried

out or installed before selecting design current conditions. Reliable methodsfor obtaining design current conditions for a given deep #ater location haveyet to be developed, only a brief discussion of this topic is given herein.

/t is sho#n, through calculations of =/='response and simulations of typicalmarine operations, that the variability of the current #ill sometimes have asignificant e ect on the response;operation.


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-ontents

Ackno#ledgements i Abstract iii

-ontents v

&omenclature i4

: /ntroduction :

:.: The marine environment . . . . . . . . . . . . . . . . . . . . . . . .

:. 6umans and the marine environment . . . . . . . . . . . . . . . . .

:.7 %otivation for the present #ork . . . . . . . . . . . . . . . . . . . . "

:." urpose of the #ork . . . . . . . . . . . . . . . . . . . . . . . . . . ":.? Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . ?

Ocean dynamics

.: /ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B

. 0lobal ocean circulation . . . . . . . . . . . . . . . . . . . . . . . . B..: )ea #ater . . . . . . . . . . . . . . . . . . . . . . . . . . . . C

.. %echanisms driving and governing the ocean circulation . . :!..7 %ain circulation types . . . . . . . . . . . . . . . . . . . . . ::

.." 0overning equations of the ocean circulation . . . . . . . . . :7

..? %a


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vi CONTENTS

.".7 /nternal #aves interacting #ith the slope . . . . . . . . . . . 7?

."." The e ect of bottom topography . . . . . . . . . . . . . . . 7.".? The e ect of #ind. . . . . . . . . . . . . . . . . . . . . . . . 7B

.".D Turbidity currents. . . . . . . . . . . . . . . . . . . . . . . . 7C

7 -urrent measurements #est of &or#ay ":7.: /ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "

7. %easuring ocean currents . . . . . . . . . . . . . . . . . . . . . . . "

7..: 0eneral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "

7.. $irect methods . . . . . . . . . . . . . . . . . . . . . . . . . "

7..7 /ndirect methods . . . . . . . . . . . . . . . . . . . . . . . . ""

7.." Requirements to current measurements used in o shore en'gineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "?

7.7 -urrent measurement sites . . . . . . . . . . . . . . . . . . . . . . . "D

7." Eater masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "

7.? -urrent profile measurements. . . . . . . . . . . . . . . . . . . . . . "B

7.?.: $escription of current profile measurements . . . . . . . . . ?!

7.?. )ources of error . . . . . . . . . . . . . . . . . . . . . . . . . ??

7.?.7 %ain results . . . . . . . . . . . . . . . . . . . . . . . . . . . ?D

7.?." -orrelation in the vertical . . . . . . . . . . . . . . . . . . . ?B7.?.? 5O2 analysis . . . . . . . . . . . . . . . . . . . . . . . . . . ?C

7.?.D A closer look at some strong current events . . . . . . . . . . D

7.D &ear'bed current measurements. . . . . . . . . . . . . . . . . . . . .

7.D.: Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

7.D. /ntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . 7

7.D.7 2lo# measurements. . . . . . . . . . . . . . . . . . . . . . . "

7.D." ostprocessing and data analysis. . . . . . . . . . . . . . . . D

7.D.? 0lobal properties of the flo#. . . . . . . . . . . . . . . . . . C

7.D.D -urrent flo# events. . . . . . . . . . . . . . . . . . . . . . . C

7.D. )ummary and conclusion. . . . . . . . . . . . . . . . . . . . C:

7.D.B -urrent meter mooring vibrations . . . . . . . . . . . . . . . C7

7.D.C Ackno#ledgements. . . . . . . . . . . . . . . . . . . . . . . . C"

" &umerical simulations of flo# dynamics on the continental slopein a t#o'layered ocean C

".: /ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CB

". &umerical ocean modeling . . . . . . . . . . . . . . . . . . . . . . . CB

".7 3ackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CB

"." &umerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . CC".".: 0overning equations . . . . . . . . . . . . . . . . . . . . . . CC

".". 0eometry, discreti@ation and initiali@ation . . . . . . . . . .:!:

".".7 3oundary conditions . . . . . . . . . . . . . . . . . . . . . . :!7

".? Results from numerical simulations . . . . . . . . . . . . . . . . . . :!?


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CONTENTS vii

".?.: Results using a #ave'shaped initial perturbation . . . . . . . :!?

".?. Results using an initial depression of the pycnocline . . . . . :!D".D -omparison #ith laboratory e4periments . . . . . . . . . . . . . . . ::"

? Ocean current variability applied in o shore engineering ::

?.: /ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ::B

?. hysically consistent current field . . . . . . . . . . . . . . . . . . . ::C

?.7 )tatistical description of current field . . . . . . . . . . . . . . . . . :!

?.7.: 54isting design philosophy . . . . . . . . . . . . . . . . . . . :!

?.7. %ost probable current condition . . . . . . . . . . . . . . . . :

?.7.7 robability of occurrence ' counting method . . . . . . . . . :"

?." -urrent condition for () design . . . . . . . . . . . . . . . . . . . :??.".: O set of surface vessel . . . . . . . . . . . . . . . . . . . . . :D

?.". Riser angle at top;bottom . . . . . . . . . . . . . . . . . . . :

?.? -urrent conditions for 2) design . . . . . . . . . . . . . . . . . . . :B

?.?.: 2atigue due to #aves . . . . . . . . . . . . . . . . . . . . . . :B

?.?. 2atigue due to current load *=/=+ . . . . . . . . . . . . . . . :C

?.D -urrent conditions during marine operations . . . . . . . . . . . . . :7!

?. 54treme events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :7:

?.B $esign current conditions based on measurements . . . . . . . . . . :7

?.B.: )tatistical analysis and reconstruction of current conditions . :77

?.B. -haracteristic parameters of current conditions . . . . . . . :7"?.C $esign current conditions ' a simple model . . . . . . . . . . . . . . :7?

?.C.: %otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . :7?

?.C. Relevant information . . . . . . . . . . . . . . . . . . . . . . :7?

?.C.7 -onsiderations and assumptions . . . . . . . . . . . . . . . . :7D

?.:! $esign current conditions ' direct simulations. . . . . . . . . . . . . :7B

D )ome e ects of current flo# variations on marine structures and

operations :":

D.: /ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :"

D. =/= of free span pipeline . . . . . . . . . . . . . . . . . . . . . . . . :" D..:

/ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . :"D.. -urrent data . . . . . . . . . . . . . . . . . . . . . . . . . . :""

D..7 =/='analysis procedure . . . . . . . . . . . . . . . . . . . . . :""

D.." 5 ect of inclined flo# on =/= . . . . . . . . . . . . . . . . . :?!

D..? -ase studies . . . . . . . . . . . . . . . . . . . . . . . . . . . :?

D..D Results, discussion and conclusions . . . . . . . . . . . . . . :?"

D.7 %arine operations in deep #ater in a variable current flo# environment:?

D.7.: /ntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . :?

D.7. -urrent flo# input . . . . . . . . . . . . . . . . . . . . . . . :?B

D.7.7 )imulation of marine operations . . . . . . . . . . . . . . . . :D!

D.7." Results and discussions . . . . . . . . . . . . . . . . . . . . . :D"


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viii CONTENTS

D.7.? -onclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . :D

-onclusions and recommendations for further #ork ::.: -onclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :

.:.: -urrent variability . . . . . . . . . . . . . . . . . . . . . . . :

.:. O shore engineering in a variable current environment . . . :7

. Recommendations for further #ork . . . . . . . . . . . . . . . . . . :7

References :?

Appendices :BB

A 5quations and solution techniques for a $ σ 'coordinate numeri'

cal ocean model. :BC A.: /ntroduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . :BC

A. -oordinate systems. . . . . . . . . . . . . . . . . . . . . . . . . . . :C!

A..: -artesian coordinate system. . . . . . . . . . . . . . . . . . . :C!

A.. σ 'coordinate system. . . . . . . . . . . . . . . . . . . . . . . :C! A..7 )ome rules for di erentiation. . . . . . . . . . . . . . . . . . :C!

A.." Total derivative in the σ 'coordinate system. . . . . . . . . . :C: A..? =ertical velocity in the σ 'coordinate system. . . . . . . . . . :C

A.7 0overning equations. . . . . . . . . . . . . . . . . . . . . . . . . . . :C

A.7.: The equations in the cartesian coordinate system. . . . . . . :C A.7. σ 'coordinate equations. . . . . . . . . . . . . . . . . . . . . . :C"

A." )olution technique . . . . . . . . . . . . . . . . . . . . . . . . . . . :C

A.".: &umerical grid . . . . . . . . . . . . . . . . . . . . . . . . . :C

A.". %ode splitting . . . . . . . . . . . . . . . . . . . . . . . . . . :C

A.".7 Time integration . . . . . . . . . . . . . . . . . . . . . . . . !!

3 =/= analyses of free span pipelines !7

- Results from simulations of marine operations ::


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&omenclature

0eneral Rules

• )ymbols are generally defined #here they appear in the te4t for the firsttime.

• )ymbols for vectors and matrices are #ritten in bold face.

Roman symbols

u #ater particle speed in 4'direction v #ater particle speed in y'directionw #ater particle speed in @'direction

U time averaged #ater particle speed in 4'directionV time averaged #ater particle speed in y'directionW time averaged #ater particle speed in @'directionu fluctuating #ater particle speed in 4'direction

v fluctuating #ater particle speed in y'directionw fluctuating #ater particle speed in @'directionT #ater temperatureT time averaged #ater temperatureT fluctuating #ater temperatureS #ater salinityS time averaged salinityS fluctuating salinityp pressure

pH hydrostatic pressure

p non'hydrostatic pressure correction

i4


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4 NOMENCLATURE

R Rossby radius of deformation

R I /nternal deformation radiusN buoyancy frequency, 3runt'=FaisFalF frequencyP

atm atmospheric pressure

i √

comple4 unit, i > −:V

c mean flo# speed(

H mean hori@ontal velocity vector

qm*t + hori@ontal velocity vector in comple4 notationbm*4+ the mGth empirical orthogonal function *5O2+

#m*t + the mGth principal componenta

nm comple4 representation of hori@ontal velocity vector

B matri4 of 5O2sW matri4 of principal components

A matri4 of comple4 hori@ontal velocity vectors

covariance matri4 for principal components

Λ eigenvalue matri4

C covariance matri4 for hori@ontal velocity vectorsH velocity vector parallel #ith the sea floor at(P i,

time instance i in 62 time'trace no. .T mean temperature in 62 time'trace no. .V

P mean flo# speed parallel #ith the

sea floor in 62 time'trace no. .V M A! ma4imum flo# speed parallel #ith the

sea floor in 62 time'trace no. .V

RM S root mean square of the flo# speed parallel #ith

the sea floor in 62 time'trace no. .f -oriolis parameter

g acceleration of gravity

C v heat capacity of sea#ater at constant volume AM hori@ontal eddy viscosity" M vertical eddy viscosity

AH hori@ontal eddy di usivity" H vertical eddy di usivityR i gradient Richardson number # M 2 semi'diurnal principal lunar frequency *M +=P mean velocity vector parallel

#ith the sea floor for 62 time'trace no. .# v vorte4 shedding frequency

St )trouhal number R$ Reynolds number D diameter of sphere or pipe


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NOMENCLATURE 4i

% & , % ' , % ( )w

* +

)+

H

c !

Sm

Smm p-$

$T

V H V

H 1

p*v, . +H

# C% H

# IL

# /0c,C%# 0w H

# 0w H

# 0w,IL

E &,# /0c

U R

parameteri@ed friction forces in numerical oceanmodel amplitude of #ave'shaped perturbation

of the pycnocline in numericalmodel length of initial depression of pycnocline in numerical modelheight of initial depression ofpycnocline in numerical modeldepth of undisturbed #ater columnlinear speed of long internal

#aves in a t#o'layer fluid

independent scatter diagram

conditional scatter diagram

matri4 of cell numbers

measure of vertical variation of hori@ontal stiness :! minute mean hori@ontal speed

$ probability density function for V H 1 and . H 1 non'dimensional frequency for cross'flo#oscillations non'dimensional frequency for in'lineoscillations cross'flo# oscillation frequency

eigenfrequency in still #ater non'dimensional eigenfrequency in still #ater

non'dimensional in'line eigenfrequency in still#ater e4citation parameter for oscillationfrequency # /0c reduced veloctiy


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4ii NOMENCLATURE

0reek symbols

1*T , S, p+ density of sea#ater

σ t > 1*T , S, !+ in 0itu density #hen the pressure e ect is ignored 1 density variation of sea#ater 1! reference density of sea#ater

2 # thermal conductivity of sea#ater 2 T heat di usivity of sea#ater 2 S salt di usivity of sea#ater dissipation rate per unit mass, Im0−7J 1i3 comple4 correlation coe cient bet#een velocity vectors

. P mean direction of the flo# that is parallel#ith the sea floor for 62 time'trace no. .

4w length of #ave'shaped perturbationof the pycnocline in numerical model

. H 1 :! minute mean flo# direction5 ratio bet#een #eight in #ater and drag force6 bottom stress7 surface elevation

σ n standard deviation of noise in 62 measurements8 m 1ronecker delta9 internal #ave frequency9 #ave frequency

: dynamic molecular viscosity, Ikgm−:s−:J; kinematic molecular viscosity, ; > :


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e4pected valueI>J


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!hapter 1

/ntroduction

:


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CHAPTER ?@ INTRO+UCTION

:.: The marine environment

Appro4imately !L of the surface on 5arth is covered by oceans. /t is customary

to consider the )outhern Ocean *Antarctic Ocean+, the Atlantic Ocean, the acific

Ocean, the /ndian Ocean and the Arctic Ocean to be the main oceans. Other bod'

ies of #ater, or portions of oceans, are usually given the term GseaG. Among these

are the %editerranean )ea, the -aribbean )ea, the &or#egian )ea, the abrador

)ea, the Eeddell )ea, the -hina )eas and the Tasman )eas.

These oceans and seas, their dynamics, biology, physiology and chemistry, is#hat constitute the marine environment.

:. 6umans and the marine environment

6umans have interacted #ith the marine environment for thousands of years. Ac'tivities such as fisheries, e4ploration, trade and #ar started early. Archaeological investigations have provided evidence that there #as a #ellestablished trade'port in othal in /ndia as early as "!! 3.-.

5arly sea'farers, such as the hoenicians, 5gyptians, Arabs, 0reek and olyne'

sians, started to collect information about the oceans around :?!! 3.-. 2or a longtime, navigation, trade and mapping the Eorld #as the main concern for thesesailors. )ince then, our kno#ledge of the oceans has increased gradually.

$uring the %ing dynasty the -hinese e4plored the -hina )eas and the /ndian

Ocean using their unique Gtreasure fleetG: *evathes :CC+. They concluded, ho#'

ever, that nothing of significance #as to be found outside of their borders, and, asa consequence, isolated themselves until #ell into the nineteenth century.

At the end of the :?th century, a series of important ocean voyages #ere initiated.

The primary reasons for these voyages #ere, then, as they are no#, economicaland political. After a #hile it became clear that good kno#ledge of the ocean could

be of good use in #ar and trade, and the desire to e4plore many aspects of the

oceans lead to a mulititude of ne# discoveries. )ailing routes from 5u'rope to

-hina, /ndia and the Eest'/ndies #ere discovered by =asco da 0ama and

:The -hinese treasure fleet, under the command of eunuch admiral Mheng 6e, sailed the

seas bet#een :"!? and :"77. This #as a unique armada at the time. The largest ship in thefleet #as four hundred feet long and had nine masts. /n comparison, the )anta %aria, used by-olombus on his first


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?@@ HUMANS AN+ THE MARINE ENVIRONMENT 7

-hristopher -olombus7. %uch #as contributed to the development of charts

by the circumnavigations of 2erdinand %agellan *from :?:C to :?+ and )ir 2rancis $rake *from :? to :?B!+. ater, the voyages of -aptain 9ames -ook*bet#een :DB and :C+ provided more accurate charts than before, chartsof ne# areas and also observations of #inds, current and #ater temperatures.

/n :! 3en


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" CHAPTER ?@ INTRO+UCTION

:.7 %otivation for the present #ork

%arine structures in the ocean are e4posed to forces from hydrostatic pressure,

temperature di erences, #aves and current flo#. 2or certain spatial and tempo'ral

scales, these environmental loads vary in either time or space or both. Eave

forces are important in the splash @one and on short time scales *minutes, sec'

onds+. 3elo# the splash @one, ho#ever, the global response of slender structures

such as risers, umbilicals and intervention lines is in some cases governed by the

current flo#. /n other cases the response can be indirectly governed by the

surface #aves through the motions of one or more surface vessels attached to

the slen'der structure. The spatial current variations in the ocean cover all scales

from basin #idth to microscale, and temporal variations occur on periods fromseconds to years. The variations containing su cient energy such as to be

important for marine structures;operations normally occur on scales larger than

those of surface #aves.

Traditionally, the o shore engineer assumes the current flo# velocity to be con'

stant in time #hen calculating dynamic response of marine structures or #hen

planning and preparing for marine operations. As #ater depths increase, ho#ever,

the current flo# #ill be increasingly important in the analysis of global response of

slender structures. %ooring lines, risers, umbilicals and intervention lines may

span a large area #hen oil and gas fields are being developed at large #ater

depths. /f this area becomes large enough, using only a constant *in space+

current profile, may not be enough to model the current #ith su cient accuracy.

2urthermore, comple4 marine operations at these large #ater depths may require

such a large time #indo# that flo# speed and direction have time to change

significantly dur'ing the operation. /n the case that the current load on cables,

intervention lines or hanging loads is of significance during critical moments of a

marine operation, then variations of the current velocity could result in unforeseen

and, possibly, un'#anted events. /ndeed, such events have already caused

increased cost and added comple4ity to marine operations.

/t is the increased importance of the spatial' and temporal variations in thecurrent flo# as the o shore engineering activity moves to#ards larger #ater depths that is the motivation for the present #ork.

:." urpose of the #ork

Ehen one is involved in the design of marine structures, or the planning of marine operations, for a certain o shore location one must find satisfactoryans#ers to the follo#ing questions N

B Ehat is the current flo# like in the area


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?@@ OUTLINE O% THE THESIS ?

B 6o# is the structure;operation a ected by this current

There are, of course, several other issues that require attention and may bemuch more important than those mentioned above. The purpose of this #ork,ho#ever, is to shed some light on the issues raised by these t#o questions.

The circulation of #ater in the EorldGs oceans vary from one location to thene4t. reviously, most of the o shore activity #as taking place on thecontinental shelf. &o#, ho#ever, more and more of this activity take place onthe slope from the shelf edge to the deep #ater. Therefore, in an e ort toaddress the issues stated above, the focus #ill be on the variability in time and

space of the current flo# near and above the continental slope and its e ect onmarine structures;operations in that area.

:.? Outline of the thesis

An overvie# of the global circulation of #ater in the oceans, and the governing

mechanisms, can be found in chapter . At several locations in the ocean *al'most

every#here+, local variations in the current flo# e4ist on a variety of time'and

length scales. An account of the properties of some of these variations, and of themechanisms responsible for them, is given in section .7.:. -ertain areas of the

EorldGs oceans have special and characteristic features to its current flo#. The

features of some of these areas, particularly those interesting for the o shore

industry, are described in section .7.. 2inally, a detailed description of some

processes taking place on the slope from the continental shelf to the deep ocean

*the continental slope+ is provided in section .".

-hapter 7 contains a description of ocean current measurements, carried outat some locations on the continental slope outside %id'&or#ay, and a

discussion of the results. %easurements of flo# velocity in the entire #ater coloumn at t#o loca'tions are presented. These measurements #ere carriedout using averaging periods of :! and 7! minutes. /n addition to these data,recordings of current velocity and #ater temperature at four locations near asmall under#ater hill, sampled at : 6@, are reported.

A numerical study on the velocities that occur #hen internal #aves on a deep

pycnocline? encounter an idealised continental slope is reported in chapter ". An

e4isting numerical ocean model is modified and used for this study. The results

?pycnocline>density surface bet#een #ater masses. The pycnocline bet#een t#o #ater

masses of di erent density is defined by the ma4imum of the density gradient.


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!hapter 2

Ocean dynamics


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B CHAPTER @ OCEAN +DNAMICS

.: /ntroduction

The oceans are important to human life. They provide the home for large quanti'

ties of natural resources *food end energy+, they are a key element in transporting

these goods, other goods and people, and they are very important for the climate

on 5arth. 3ecause of the importance of the oceans, it is in our interest to learn as

much as possible about them. Oceanography is defined as the scientific study of

the oceans. /t is customary to consider this science to comprise the fields of

physical oceanography, chemical oceanography, biological oceanography and

geo'logical oceanography. Researchers #ithin theses fields study the #ater

masses in the oceans. The #ater masses in the oceans contain many di erent

ingredients, such as sediments, chemicals and living organisms. Theseingredients are being transported by the ocean currents. The ingredients in the

sea #ater determine the density of the #ater, #hich is important for the

development of ocean currents. iving organisms in the ocean depend upon

nutrients being transported by the ocean currents. 2or these reasons, along #ith

several other reasons, researchers #ithin one of the fields of oceanography often

find it beneficial to cooperate #ith those #orking in one *or more+ of the other

fields. Thus, the various fields of oceanography cannot be vie#ed as entirely

isolated from one'another, they are related.

The focus in this thesis is on the current flo# in the ocean, a sub


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@@ LOFAL OCEAN CIRCULATION C

The mechanisms governing the large scale flo# of #ater in the #orld oceans, to'

gether #ith the ma


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:! CHAPTER @ OCEAN +DNAMICS

Observations of temperature and salinity of the #ater in the main three oceans

*Atlantic, acific and /ndian+ suggest the e4istence of :C di erent #ater masses in the upper ?!! meters *5mery and %eincke :CBD+. $i erences intemperature and salinity from one #ater mass to another occur for severalreasons. Temperatures vary due to heating on the surface by the sun, heatingthrough the sea bed, up';do#n #elling of #ater near a coast, transport of #ater by the ma


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@@ LOFAL OCEAN CIRCULATION ::

ever, the relative direction bet#een #ind and current flo# is appro4imately :B!/. An

5kman layer is also formed at the sea bed #hen friction acts on the #ater flo#ing

above the sea bed. The transport in the bottom 5kman layer is to the left of the

direction of the undisturbed flo# *on the northern hemisphere+. Another feature of the

combined e ect of friction and rotation is the intensification of the current flo# at the

#estern boundaries of all oceans. There are strong currents #ith high shear in the

#est of the main oceans, but slo#er currents #ith much less shear in the eastern part

of the same oceans. The e4planation of this P#est#ard in'tensificationG of the flo# #as

provided by )tommel *:C"B+ and is directly linked to the rotation of the 5arth and

friction bet#een the flo#ing #ater and the coast. 5k'man veering and #est#ard

intensification are features of the large scale circulation.

..7 %ain circulation types

0enerally, the large scale circulation of #ater in the oceans is characteri@ed aseither thermohaline or #ind driven. These t#o types of circulation cover theflo# of #ater in the deep ocean and in the upper layers, respectively.

Thermohaline circulation

0ravitation is a primary force, acting on the #ater in the ocean. As #e have al'ready

mentioned, the distribution of temperature and salinity *and thus density+ in theoceans is not homogenous. 2or large parts of the ocean the vertical #ater coloumn

can be divided into three parts according to the distribution of #ater temperature. /n

the upper @one *from the surface to a depth of ?!'!! meters+7 the #ater is #ell

mi4ed and the temperature is fairly constant. 3elo# this @one *!!':!!! meters+ the

temperature decreases rapidly. /n the deep @one *belo# :!!! meters+ the

temperature decreases slo#ly. )ee 2igure .: for an illustration. The thermocline is

located in the @one #here the temperature is decreasing rapidly *the thermocline

@one+, at the depth #here the temperature gradient is at its ma4imum, see 2igure .:.

Observations indicate that the thermocline *@one+ e4ist continously and at more or

less the same depth at a given location in latitudes from about !/ to "!

/ &orth and

)outh. /n order for this to be possible, cold #ater must flo# in from belo# to

counteract the e ect of heating from the sun on the surface. /t is believed that this in'

flo# of cold #ater is provided by the thermohaline circulation.

&ear the equator, and at mid'latitudes, the surface #ater is heated by the sun.-ooling of the #ater takes place at high latitudes in the Atlantic Ocean, increasingthe density and causing it to sink. $eep #ater then flo#s to#ards the tropics, and

7The thickness of the upper layer *mi4ed layer+ varies from one day to the ne4t and also

bet#een the seasons. /n #inter the mi4ed layer tends to be deeper than in summer. Earmingof the surface #ater during summer may sometimes cause a seasonal thermocline to appear.


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: CHAPTER @ OCEAN +DNAMICSz (m)

1 7 10 13 Temperature

Winter Summer (seasonal thermocline)

Mixed layer

-200

Thermocline

-1000

Deep zone

-2000

2igure .:N V$-tica* t$mp$-atu-$ p-/#i*$ in t)$ /c$an t'pica* #/- miJ*atituJ$0@

the #armer #aters in the upper layer flo# from the tropics to#ards higher latitudes.

This is the essence of the theory of the large scale thermohaline circulation as it #asput for#ard by )tommel *:C?B+. /t is believed that there are t#o Pdeep #ater factoriesG

in the Eorld. One is east of 0reenland and the other one is in the Eeddel )ea in the

Antarctic. $eep #ater from these sources flo# into the Atlantic Ocean, the acific

Ocean and the /ndian Ocean. The full details of the thermohaline circulation are not

yet kno#n, but it is believed that the mechanism is responsible for the relatively slo#

current flo# in the deep @one *belo# :!!! meters+.

Eind driven circulation

Ehereas the thermohaline circulation transports #ater vertically and hori@ontally,

the #ind'driven circulation is considered to be mainly hori@ontal". The #inds in the

atmosphere are driven by solar energy. 2riction bet#een the #ind, blo#ing alongthe ocean surface, and the ocean surface itself, transfers energy into the surfacelayer of the ocean, and the #ater in this layer start to move. 2riction forcesbet#een the moving #ater in the upper layer and the #ater immediately belo#,causes the #ater in the lo#er layer to also start moving, and so on. Thus, the eect of the #ind stress on the surface causes the upper layer of the ocean to

")ome of the consequences of the #ind driven circulation, such as 5kman pumping and

up';do#n#elling, ho#ever, involve vertical transport of #ater, see section .".?


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@@ LOFAL OCEAN CIRCULATION :7

move. /t is the #ind stress that is the ma


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-onservation of mass requires that

1

Q * 1u+ Q * 1v + Q * 1w + > !, *.?+

t &

'

(


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:" CHAPTER @ OCEAN +DNAMICS

often referred to as the c/ntinuit' $quati/n, and the first la# ofthermodynamics yields the energy equation,


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1C v +T Q p u Qv

Qw > 2 # ∇T *.D+

+t & '

(

#here C v is the heat capacity at constant volume, T is the absolute temperatureand 2 # is the thermal conductivity of the fluid. -onservation of salt requires that

+S > 2 *.++t

S ∇ S

#here 2 S is the coe cient of salt di usion.

5quation of state for sea#ater

The equation of state for sea#ater gives the relation bet#een density,pressure, temperature and salinity, and is needed in order to close the set of equations. 0enerally, the equation of state is given as,

1 > 1* p, T , S+ *.B+

The 3oussinesq appro4imation

The governing equations can be simplified by using the assumption that

1* &, ', (, t + > 1! Q 1 * &, ', (, t + *.C+

1 GG 1!

#here 1 is the density variation. This is the 3oussinesq appro4imation. Applyingthis, and introducing the kinematic molecular viscosity, ; > : u > − − Q ; ∇w *.:++t 1!(

1!

/ncompressible fluid

/t is customary to introduce the appro4imation that sea#ater is incompressible,i.e. that 1

:

+1+t > !. The continuity equation *.?+ is then reduced to an

equation for conservation of volume,

u

Qv

Qw

> ! *.:7+

&

'

(


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@@ LOFAL OCEAN CIRCULATION :?

and the energy equation reduces to

+T > 2 T ∇T *.:"+

+t #here 2 T > is the heat di usivity. The equation for conservation of salt,

ho#ever, remains the same as before.

The pressure term in the equation of state is removed #hen the appro4imationof incompressible fluid is made, and the equation of state becomes,

1 > 1*T , S+ *.:?+

-onsiderations about the scale of the flo# and Reynolds averaging

2urther simplifications can be made by considering the relative magnitude of the terms in the equations, and neglecting those that are significantly smaller than the others.

The hori@ontal scale, L, of the ocean is much larger than the vertical scale, H ,i.e. H GG L. 2rom the continuity equation in its reduced form *equation .:7+ itis then possible to deduce that the hori@ontal flo# velocities in the ocean aremuch larger than the vertical flo# velocities *i.e. u, v w + #hen large scale flo#sare considered. Temporal variations of the same magnitude as the timerequired for one rotation of the 5arth *or larger+ are of interest #hen #e

consider the global circulation in the oceans, i.e. T LS Q K−:

and u


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#here U , V , , S and T are mean components and u , v , w , S and T arefluctuating parts #ith @ero mean.

/nserting *.:D+ into the governing equations, and then taking the time average,#e obtain a ne# set of equations. These can be further simplified by applying the

large scale requirements *u, v w , T LS Q K−: and u


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U U AM > −u u AM

U ' > −u v " M > −u w & (


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:B CHAPTER @ OCEAN +DNAMICS

60oN

Current

East Greenland

Labrador

Current

30oN

0o

StreamCurrent

Gulf

Florida

AntillesCurrent

Guiana

North Atlantic CurrentCurrent

Canary

North Equatorial Current

CurrentNorthBrazilEquatorialCounterCurrent

GuineaCurrent Current

SouthEquatorial

Current

30oS

BrazilCurrent

Benguela

Current

Current

Malvinas

AgulhasCurrent

60oS

Antarctic Circumpolar Current

75oW50

oW25

oW 0o 25

oE

2igure .N Ma3/- 0u-#ac$ cu--$nt0 in t)$ At*antic Oc$an@


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@@ LOFAL OCEAN CIRCULATION :C

)tramma *:CC!+.

On the northern hemisphere the norteasterly trade #inds drive the N/-t) Equat/-ia* Cu--$nt to#ards the #est. This current is


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! CHAPTER @ OCEAN +DNAMICS

• S/ut) Equat/-ia* Cu--$nt . This current flo#s from east to #est, driven bythe southeasterly trade #inds on the southern hemisphere.

• N/-t) Equat/-ia* C/unt$- Cu--$nt . This current flo#s from #est to east inthe calm belt bet#een the southeasterly and the northeasterly trade #indsystems. The current is driven by the pressure gradient #hich occur frompile'up of #ater in the #estern acific due to the trade #inds.

• S/ut) Equat/-ia* C/unt$- Cu--$nt . This current flo#s from #est to east. /tis #eak in comparison #ith the other equatorial currents.

On the northern hemisphere, the main part of the &orth 5quatorial -urrent turns north

and, soon after#ards, north'east to become the "u-i/0)i Cu--$nt , see 2ig'ure .7.The 1uroshio -urrent is a #estern boundary current, and it can be vie#ed

60oN

Current

OyashioAlaska Current

North Pacific Current

KuroshioCurrent

30oN

California

Current

North Equatorial Current

Equatorial Counter Current

0oSouth Equatorial Current

30oS

East Australia Current

Current

Peru

60oS

Antarctic Circumpolar Current

120oE 160

oE 160

oW 120

oW 80

oW

2igure .7N Ma3/- 0u-#ac$ cu--$nt0 in t)$ Paci#ic Oc$an@


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@@ LOFAL OCEAN CIRCULATION :

as the acific counterpart to the 2lorida -urrent *or vice versa+. The 1uroshio

-urrent flo#s northeast#ards along the east coast of 9apan, but eventually itleaves this coastline, in the same #ay as the 2lorida -urrent leaves the coastof &orth America to become the 0ulf )tream. The 1uroshio -urrent, ho#ever,becomes the "u-/0)i/ E&t$n0i/n, flo#ing mainly to#ards east. This current isthen


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CHAPTER @ OCEAN +DNAMICS

commonly kno#n as the 5l'&ino phenomenon.

.7 ocal variability of the circulation

.7.: Eaves, instabilities, *."+ #

#here 6 is the #ater depth, # is the -oriolis parameter, defined in section..", and K is the acceleration due to gravity.

3arotropic instability.

)mall perturbations to a barotropic flo# #ith a hori@ontal shear may gro# andbecome large if the shear is su ciently large. This phenomenon is kno#n asbarotropic instability, and causes lo#'frequency oscillations to the flo#.

1elvin'6elmholt@ instability.

A t#o'layer hori@ontal flo#, separated by a thin interface #ith one layer heavier

than the other and flo#ing at di erent speeds, is al#ays unstable, 1undu *:CC!+.

This is the original 1elvin'6elmholt@ instability, and it is responsible for the gen'

eration of the #ind'induced surface #aves of the oceans. /n the ocean interior #e

rarely find a thin interface bet#een t#o fluid layers. /nstead, a continous strati'

fication is mostly seen. /nstabilities in hori@ontal parallell flo# #ith a continous

stratification is also referred to as "$*vinH$*m)/*t( in0tai*it' . %iles *:CD:+ and6o#ard *:CD:+ have sho#n that such a flo# is unstable #hen

− K J1N

:

R i > 1 J( > G *.?+

* JU

+

* JU

+

"J( J(


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@@ LOCAL VARIAFILITD O% THE CIRCULATION 7

#here U is the undisturbed shear flo# and 1 is the undisturbed density field.The stratification is e4pressed by the 3runt'=FaisFalF frequency, N , alsokno#n as the buoyancy frequency. )trong stratification and;or #eak currentshear prevents instability. The ratio bet#een the buoyancy frequency *i.e. thestratification+ and current shear is given by the gradient Richardson number,

R i , and it can be vie#ed as a ratio bet#een potential and kinetic energy.

9ets, 5ddies and turbulence.

$ensity fronts e4ist at locations #here t#o di erent #ater masses meet. Theflo# along such fronts is driven by the hori@ontal pressure gradient, #hich islarge in such areas, and geostrophically ad


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" CHAPTER @ OCEAN +DNAMICS

describe the turbulent velocity field #ithout the aid of statistical methods, see

e.g. 3radsha# *:C?+.

Tides.

The gravitational pull from the sun, the moon and of 5arth itself on the #ater inthe oceans, and the relative motion bet#een the sun, the moon and 5arth,causes a cyclic rise and fall of the sea surface. These are the tidal changes,and they vary #ith periods of appro4imately :':7 hours *semi'diurnal+ insome places and about "'? hours *diurnal+ in other places. There areseveral tide'producing constituents, see e.g. ond and ickard *:CB7+, and

their relative phase and ampli'tude varies for di erent locations. 6ori@ontalcurrent flo# speed associated #ith the tidal rise and fall are generally larger near the coast than in the open ocean. arge speeds * ? m;s+ may occur #hen the tide enters or e4its through narro# passages. /n the open ocean,ho#ever, the flo# due to the rise and fall of the tide is O*!.: m;s+.

Ehen the tidal #ave encounter the continental shelf or slope in a stratifiedocean, internal #aves may be generated. /nternal #aves are supported by thevertical stratification in the ocean. -hapter " of this thesis contains more onthe sub


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@@ LOCAL VARIAFILITD O% THE CIRCULATION ?

described in this section.

The internet site at httpN;;oceancurrents.rsmas.miami.edu;inde4.html #asfrequently used during the #ork #ith this section.

0ulf of %e4ico

T)$ Ca-i$an Cu--$nt is the main surface current in the -aribbean )ea. Ea'ter from the &orth 5quatorial -urrent, the &orth 3ra@il -urrent and the 0uiana-urrent *see 2igure .+ enters through the passage bet#een the esser Antilles in the southeast. At first, this #ater flo#s #est#ards into the -aribbean

)ea. ater on, the current shifts to#ards north#est and flo#s into the 0ulf of %e4ico as the Ducatan Cu--$nt , see 2igure .". A small part of this currentflo#s #est#ards over the -ampeche 3ank, but the main part flo#s to#ardsthe nort#est and thus consi'tute the start of the L//p Cu--$nt . This is a current#hich makes a characteristic loop into the 0ulf of %e4ico before it e4itsthrough the 2lorida )traits as part of the 2lorida -urrent, see 2igure .".

The oop -urrent intrusion into the 0ulf of %e4ico varies in si@e. )ometimes itcan reach as far north as C degrees, #hereas the flo# at other times is

almost directly from the Yucatan -hannel to the 2lorida )traits. AnticyclonicD

eddies *#arm rings+, typically ?!'"?! km in diameter and up to :!! metersdeep, sometimes separate from the oop -urrent and propagate#est#ards;south#est#ards, see e.g. 5lliott *:CB+ and 6amilton et al. *:CCC+.)uch #arm rings prevail for months in the 0ulf of %e4ico, and are importantfor the heat and salt budget and the general circulation in the #estern part of the 0ulf. The oop -urrent intrusion into the 0ulf is often reduced significantlyafter a #arm ring has been separated, but this is not al#ays the case. 5lliott*:CB+ found a #arm ring #hich separated from the oop -urrent in the #inter #ithout causing a #ithdra#al of the oop -urrent from the 0ulf.

A significant amount of research has been carried out on the oop -urrent, anticy'

clonic eddies and the resulting dynamics of the circulation in the 0ulf of %e4ico.=ukovich *:CBB+ studied infrared images of the 0ulf, taken over a :?'year period. 6e

found that the frequency of separation of #arm anticyclonic rings from the oop

-urrent is highly variable, but estimated an average period of :!.C months bet#een

separations. AR0O)'tracked drifting buoys are used for studying the circulation in the

0ulf in the summer #hen the #ater temperature in the upper layers is uniform and,

thus, rendering infrared images from satellites of little use. 0lenn and 5bbesmeyer

*:CC7+ studied the paths of such buoys. They found that

D-yclonic circulation is the term used for the flo# around a lo# pressure system, either in

the ocean or in the atmosphere. On the northern hemisphere the cyclonic circulation iscounter'clock#ise *seen from above+. Anticyclonic circulation is the opposite *clock#ise+.


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D CHAPTER @ OCEAN +DNAMICS

35

o

N

Gulf Stream

30oN

Loop Current

Warm ring

Florida Current

25oN

Yucatan Current

20oN

15oN

Caribbean Current

10oN 96

oW 90

oW 84

oW

78oW 72

oW

2igure ."N La-K$0ca*$ cu--$nt patt$-n0 in anJ a-/unJ t)$ u*# /# M$&ic/@

the eddies propagated in a series of short sprints separated by longer stalls.The speed of one of the eddies during one such sprint #as as high as :C

cm;s. A similar study #as conducted by 6amilton et al. *:CCC+ #ho detectedno appar'ent preferred paths of the eddies, neither in the main basin nor near the #estern slope, but the same stalling and sprinting behaviour as #as seenby 0lenn and 5bbesmeyer *:CC7+ #as found. 2urther, a clock#ise rotation of the ellipse a4is of the eddies #as observed. This rotation, and also the s#irlvelocities, #ere found to decay #ith time.

=ukovich *:CBD+ observed cyclonic cold perturbations *typically :!!'?! km in

diameter+ to the south'southeast#ards flo#ing oop -urrent close to the Eest 2lorida

)helf. Associated #ith these cold perturbations #ere #arm filaments of north#ards

flo#ing oop -urrent #ater to the #est of the cold perturbations. 2lo# speeds as high


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as :!! cm;s #ere estimated at certain places in these filaments. -old perturbations

are most pronounced on the northern and eastern boundaries of the


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@@ LOCAL VARIAFILITD O% THE CIRCULATION

oop -urrent.

The o shore structures in the 0ulf of %e4ico have been designed for the relatively

large current flo# speeds *:!! cm;s+ that occur inside the anticyclonic eddies, andin relation #ith the high variability *smaller scale cyclones and anticyclones+ that

accompanies these eddies, or are generated by them. /n the o shore indus'try, an

anticyclonic eddy is termed EJJ' Cu--$nt . The anticyclonic eddies are only present inthe upper :!!! ' :!! meters of the #ater column in the 0ulf. 6amilton *:CC!+

analy@ed measurements of current velocity from belo# :!!! meters in the eastern,

central and #estern parts of the 0ulf and found evidence of topographic Rossby

#aves propagating to#ards the #est. 2luctuations of the oop -urrent #ere identified

as the source of these #aves, something #hich )turges et al. *:CC7+ also observed intheir numerical simulations. /n a later study, 6amilton and ugo'2ernande@ *!!:+

observed velocities greater than B? cm;s close to the seabed at a depth of

appro4imately !!! meters close to the )igsbee 5nscarpment at the base of the

continental slope in the northern 0ulf of %e4ico. =igourous *∼"! to ?! cm;s+ near'

bottom currents #ere seen to occur as part of nearly continous #ave trains passing

through the area. /t #as suggested that such deep energetic disturbances are

generated by the passage of cyclonic eddies in layers higher up, and theat these

disturbances travel #est#ards as topographic Rossby #aves.

Eest of )hetland

The &orth Atlantic -urrent splits into t#o ma


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B CHAPTER @ OCEAN +DNAMICS

The slope currents along the 2aeroe')hetland -hannel and along the shelf edge

outside &or#ay can be vie#ed as


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@@ LOCAL VARIAFILITD O% THE CIRCULATION C

70

o

N

65oN

NorwegianAtlantic Current NorwegianWestern branch Atlantic Current

Eastern branch

Iceland−Faroe

frontal jet

60oN

55oN

NorthAtlanticCurrent

Slope

Continental

Current

Troll

O

O Skagerak

Vortices

Baltic

North Sea

Sea

50oN

45oN 8

oW 0

o8oE 16

oE

16oW

2igure .?N In#*/w /# N/-t) At*antic wat$- t/ t)$ N/-Jic S$a0@ T)$ v/-tic$0/ut0iJ$ t)$ c/a0t /# N/-wa' a-$ a*0/ 0)/wn@

kind *such as the 0ulf )tream or the 1uroshio+. The 3ra@il -urrent stays mainlyon the continental margin on its #ay to#ards sout#est until it reaches appro4i'

mately 7?/). 6ere, the current meets #ith the northeast#ards flo#ing %alvinas

-urrent, leaves the east coast of )outh America and continues to#ards south to'gether #ith the return flo# of the %alvinas -urrent, see 2igure .D.

The area in #hich the 3ra@il -urrent meets #ith the %alvinas -urrent lies bet#een

7?/) and "!

/), depending upon the time of year, and is referred to as the F-a(i*

Ma*vina0 C/n#*u$nc$ *0ordon and 0reengrove :CBD+. The %alvinas -urrent is astrong *"!':!! cm;s+ flo# of cold subantarctic #ater #ith lo# salinity, #hereas the

subtropic #ater in the 3ra@il -urrent is #armer and more saline. A sharp oceanic front


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e4ist bet#een these #ater masses, resulting in the formation of cold and #arm eddies

from the %alvinas -urrent and the 3ra@il -urrent, respectively,


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7! CHAPTER @ OCEAN +DNAMICS

0o North Brazil Current

South Eq. Curr.

12oS

Current

Brazil

Vitória−Trindade Ridge

24oSCampos Basin

Cabo Frio

BrazilCurrent

36oS

Brazil−Malvinas

Confluence

48oS

Malvinas Current

60oS 72

oW 60

oW 48

oW

36

o

W 24

o

W

2igure .DN Cu--$nt patt$-n0 /ut0iJ$ F-a(i*@

see e.g. 0ar@oli and 0arra o *:CBC+.

The -ampos 3asin, #hich is located in the area around /) and "!

/E, see 2ig'

ure .D, is the most important area for o shore oil production outside 3ra@il. Thishas resulted in high priority to#ards monitoring and predicting the circulation inthe area *=ianna and de %ene@es !!"+. 0arfield *:CC!+ studied infrared images

and found eddies and meanders in the 3ra@il -urrent in this area. A cyclonic


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@@ LOCAL VARIAFILITD O% THE CIRCULATION 7:

eddy #as observed


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7 CHAPTER @ OCEAN +DNAMICS

30oN

15oN

0o Guinea Current

15oS

Angola−Benguela Front

Curre

nt

Angola

30oS

Benguela

Current

20oW 10

oW 0

o10oE 20

oE 30

oE

2igure .N Cu--$nt patt$-n0 /ut0iJ$ $0t A#-ica@

." rocesses on the continental slope.".: %otivation for focusing on the continental slope

%ost of the oil and gas e4traction around the #orld today take place on continental

shelf areas near shore. 6o#ever, some of this activity has begun to move past the

continental shelf edge. The continental shelf is the relatively flat plateau *average

gradient is :N?!!+ near shore, see 2igure .B. This plateau consists of sediments

#hich have been eroded from the continent. )uch sediments are constantly being

transported from the shore to#ards the edge of the continental shelf *also referred to

as the 0)$*# -$a +. 6ere the inclination of the bottom is increased many times. The

continental slope is located bet#een the shelf break and the deep ocean bottom andthe average inclination angle is 7 degrees *-acchione and ratson !!"+.


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@@ PROCESSES ON THE CONTINENTAL SLOPE 77

The dynamics of the fluid flo# on a continental slope, or other sloping

boundaries in the ocean, are comple4 and diverse. $uring the #ork that #ascarried out #hen establishing the metocean design basis for the developmentof the 2oinhaven'field on the continental slope #est of )hetland, 0rant et al.*:CC?+ found that the cur'rents at the site #ere Pfar more comple4 than thosetraditionally encountered by the oil industry in the shallo#er &orth )eaG.

rocesses such as e.g. up;do#n'#elling, breaking;overturning;reflection of inter'nal #aves and 5kman veering take place on the continental slope. Theseprocesses may interact, making such regions of the ocean a highly variableenvironment. A full account of these processes can be found in te4tbooks suchas those by hillips *:C+ and $e#ey et al. *:CBB+, and only a short overvie##ill be provided in this section.

The high variability seen near the continental slopes several places around the#orld is believed to be important for the global circulation in the #orld oceans*5riksen :CB?+, but it is also of interest for the design and planning of marinestructures to be placed or operated in such environments.

2or a general revie# of physical processes at ocean margins, see 6uthnance *:CC?+.

Average depth : 130 m

Continent

Shelf

edge

Typical

depth :

3000-6000 m Continental slope

Continental margin

Continental shelf

(average length : 65 km.)

(typical slope , 1:500)

Average inclination angle : 3 degrees.

Continental rise

Deep ocean bottom

2igure .BN I**u0t-ati/n 0)/winK t)$ 0$a $J n$a- t)$ c/ntin$nta* 0*/p$@


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@@ PROCESSES ON THE CONTINENTAL SLOPE 7?

and ent@ *:CC:+ and ent@ and Tro#bridge *:CC:+. 6osegood and van 6aren

*!!7+ propose that high'frequency current meter misalignment #ith the meanflo#, caused by such turbulence, is the mechanism behind the spike'likeobserva'tions, and that the intermittency of the spikes is due to the turbulentboundary layer bursting phenomenon described by 6eathersha# *:C"+,6eathersha# and Thorne *:CB?+ and uchnik and Tiederman *:CB+.

Other contributions to the topic of 5kman layers on a sloping bottom can befound in e.g %ac-ready and Rhines *:CC:, :CC7+.

.".7 /nternal #aves interacting #ith the slope

Another mechanism, leading to variations in temperature and currents near the

continental slope, is the interaction bet#een the sloping boundary and internal #aves.

/nternal #aves are gravity #aves in the interior of a fluid, supported by vertical

stratification. /n the atmosphere, such #aves can be observed by #atching cloud

formations, and in the ocean thay can in some cases be observed from high above,

e.g. satellite photos. /nternal #aves in the ocean are generally generated by

conditions at the surface *moving pressure fields, travelling #ind fields+ or at the sea

bed *flo# over topography, earthquake+. Ehen internal #aves are gener'ated by the

diurnal' or semi'diurnal tide they are often referred to as int$-na* tiJ$0.

The buoyancy frequency, defined by

N > − K J1 *.+

1! J(

is an important parameter in the study of internal #aves. Analytical solutionsfor linear, inviscid internal #aves can be found by solving a lineari@ed versionof equations *.:+'*.:C+ in #hich the Reynolds stresses are neglected and

the termw

t in equation *.:C+ is reinstated. The dispersion relation is found

by inserting solutions of the form $i **& Qm' Qn(−9t +, #here 9 is the internal #avefrequency, into the lineari@ed set of equations. 0ill *:CB+ gives the dispersion

relation for internal #aves propagating do#n#ards #ith a characteristic angle, W, as seen in 2igure .C, as9 > N sin W Q # cos W *.B+

hase speed for internal gravity #aves is defined in the same #ay as for surface gravity #aves

c > √ 9 *.C+* Q m Q n

#here the #ave number vector is defined by 2 >* i Q m < Q nk. The group velocityvector, defining the propagation direction of the internal #ave energy, is given by

cK > J9 *.7!+

J2


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7D CHAPTER @ OCEAN +DNAMICS

The vertical component of cK can be positive, @ero or negative. /f it is negative the

internal #ave energy propagates do#n#ards to#ards the sea bed. &ote that thegroup velocity vector is al#ays perpendicular to the phase velocity vector, and

that phase and energy al#ays propagates in the same hori@ontal direction, but in

opposite vertical direction. Ehen such #aves encounter the continental slope, as

sho#n in 2igure .C, they are reflected if the slope angle, X , is smaller than W. /t isassumed that the a@imuth of the #ave is @ero *i.e. the group velocity vector is

perpendicular to the isobaths+. &ote that the internal #ave reflection angle #ith

the hori@ontal is W, regardless of the slope angle *as long as X G W+. /f the internal

c

pI

cKR

Reflected c pR c

KI

Incident wave

wave

Continental

slope

W W

X

2igure .CN I**u0t-ati/n /# -$#*$cti/n /# int$-na* wav$0 /n t)$ c/ntin$nta* 0*/p$@

#ave frequency is such that W X , the internal #ave energy is trapped near the slope*according to linear theory+ resulting in unstable conditions and, possibly, strong

turbulence near the sea bed. /nteraction bet#een the incident #ave and the reflected

#ave can also cause #ave steepening, reduced stability and #ave breaking near the

slope *Thorpe !!:+. /f X W the internal #ave is reflected do#n'slope.

-acchione and ratson *!!"+ commented on the curious fact that, even though

under#ater piles of sediments can be stable #ith slopes of up to :? degrees, the

average inclination angle of the continental slope is only 7 degrees. They propose

that internal tides, and their interaction #ith the continental slope, is the primary

e4planation of this. Their argument is that the density structure of the oceans is

such that the characteristic angle of the internal tides is typically bet#een and "

degrees, and that the strong currents #hich occur at the bottom #hen the char'

acteristic angle is the same as the inclination angle of the slope actually prevents

accumulation of sediments, not allo#ing the inclination angle to become larger

than the characteristic angle.


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@@ PROCESSES ON THE CONTINENTAL SLOPE 7

2requent occurrences of inversions close to the bottom on the continental slope

south#est of /reland #ere reported by Thorpe *:CBa+, #ho attributed them to in'

stabilities of the boundary layer, possibly caused by internal #ave breaking. The flo#

patterns that occur upon reflection of internal #aves on a plane sloping bottom in a

uniformly stratified ocean has been studied by many researchers. Reflection of

internal gravity #aves at a sloping seabed #as nominated by 5riksen *:CB?+ as a

source of diapycnal mi4ing, and, thus, a possible solution to the problem of the

GmissingG vertical di usivity needed to balance the thermocline and the mean vertical

advection, 0arrett *:CC+. The turbulence and mi4ing in the boundary layer due to

interaction bet#een internal #aves and a sloping bottom has been investigated

e4perimentally by -acchione and Eunch *:C"+, Thorpe and 6aines *:CB+, /vey and&okes *:CBC+, Taylor *:CC7+ and $e )ilva et al. *:CC+. &on'linear features of the

reflection of internal #aves in a stratified fluid on a plane sloping bottom, such as

rapid changes in density and conditions favourable for #ave breaking, have been

studied in detail by Thorpe *:CBb, :CCb, :CC+. )ome results from numerical

simulations, supporting theoretical and e4perimental find'ings, have been presented

by 9avam et al. *:CCC+ and )linn and Riley *:CCB+.

/nternal #aves may be created at the shelf edge and travel do#n'slope to#ards

deeper #ater. 0emmrich and van 6aren *!!:+ observed rapid temperature re'

ductions accompanied by brief do#n'slope current events above the continentalslope in the 3ay of 3iscay, and they suggest that the stratification near the slope

is made unstable by internal #aves propagating do#n'slope. The collapse of this

unstable stratification is then observed as moving thermal fronts. -hanges in the

alongslope flo# speed from @ero to appro4imately !.? m;s #ithin :D minutes #ere

observed. This high variability can be of interest for the design and planning of

marine structures to be placed or operated in such environments.

."." The e ect of bottom topography

arge scale ocean circulation is governed by many factors, one of #hich is the bottom

topography. Topographic steering of the mean flo# is a #ell kno#n phe'nomenon

described in all te4tbooks on the sub


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7B CHAPTER @ OCEAN +DNAMICS

a relatively distinct and #ell'defined


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@@ PROCESSES ON THE CONTINENTAL SLOPE 7C

/t has been proposed that strong current events on the continental slope in thearea #est of &or#ay might be related to atmospheric conditions on the seasurface, a ecting the motion of a deep pycnocline. These events have beenobserved near the sea bed and are characteri@ed by a slo#ly increasing #ater temperature and do#n'slope flo#


60/293

"! CHAPTER @ OCEAN +DNAMICS


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!hapter "

-urrent measurements #est of&or#ay

":


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" CHAPTER @ CURRENT MEASUREMENTS EST O% NORAD

7.: /ntroduction

This chapter contains a short introduction to some methods and procedures for

measuring ocean currents in general, and some recommendations of ho# to carry

out such measurements in relation to o shore engineering in particular. $escrip'

tions of, and results from, current measurements outside the coast of %id'&or#ay

are included. 2irst, the measurement sites and the #ater masses in the area are

de'scribed, then measuremens of current profiles at t#o di erent depths are

reported. 2inally, some measurements close to the sea bed in an area #ith a

rough bottom topography are presented and discussed.

7. %easuring ocean currents

7..: 0eneral

One of the goals of the physical oceanographer is the accurate and detaileddescrip'tion of the three'dimensional temporal flo# field in the ocean, (*4 , t +. Another important goal is to obtain kno#ledge and a clear understanding of the driving mechanisms behind the observed flo#. 2ield observations are of vital importance in achieving these goals. T#o di erent types of methods for obtaining informa'tion about the ocean circulation are available, the direct

method and the indirect method.

7.. $irect methods

$irect measurements of the ocean circulation provides information about theflo# velocity at a finite number of fi4ed points in the ocean space *5ulerianflo# field+, or, alternatively, about the positions of individual #ater particles atall time *a'grangian flo# field+. The current flo# data, discussed in thischapter, are recorded by direct methods, using t#o di erent types of 5uleriancurrent measurement de'vices.

Rotor current meters

Rotor current meters for direct measurements of the flo# speed are based on

count'ing the rotations of a propeller over a time span. The orientation of the

instrument relative to the current is al#ays such that the flo# is parallel to the

propeller a4is. This is achieved by allo#ing the instrument to rotate around a

vertical a4is, gov'erned by a guiding vane. Records of current direction #as

mechanical in early rotor current meters, like the 5kman current meters, but today

the magnetic compass is used and the data are stored on digital data files.


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@@ MEASURIN OCEAN CURRENTS "7

The Aanderaa R-%' current meters, #hich #ere used for some of the measure'

ments discussed herein, calculates the vector averaged current velocity based onthe number of revolutions of a rotor and the compass direction of the instrument.

The current data are stored digitally on file inside the instrument.

Acoustic current meters

Acoustic $oppler -urrent rofilers *A$-s+ can be mounted aboard ships or held in place by mooring lines. An e4ample of such an instrument can be seenin 2igure 7.:. One A$- can record the current velocity at several depths

belo# or over its position in the #ater column. Records of flo# speeds areobtained by emitting a series of short sound #ave pulses, and then measuringand analysing the reflected signal from particles #hich travel #ith the flo#. Themethod is, thus, based upon the assumption that particles #hich aresuspended in the #ater follo# the flo#.

2igure 7.:N Ac/u0tic +/pp*$- P-/#i*$- #-/m AanJ$-aa R+CPY@ T)$ R+CPY i0 app-/&imat$*' Y cm )iK) anJ cm wiJ$@


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@@ MEASURIN OCEAN CURRENTS "?

density distribution can be obtained by measurements of salinity and

temperature for a number of locations, using equation *.:?+. The hori@ontalpressure gradient, needed to estimate U and V , can then be found from thehydrostatic pressure equation.

The geostrophic method is described in detail in most introductory te4ts onphysi'cal oceanography, see e.g. -ushman'Roisin *:CC"+, Reddy *!!:+ andickard and 5mery *:CC!+.

$istribution of #ater properties ' description method

As #e have mentioned earlier *section ..:+, it is possible to identify as manyas :C di erent #ater masses in the upper ?!! meters of the ocean *5mery and%eincke :CBD+. An indirect #ay of obtaining the flo# pattern in the ocean is totrack the di erent #ater masses by mapping the distribution of #ater properties. (sing this method, it is possible to arrive at a good qualitativedescription of the global circulation. The description is qualitative in the sensethat only information about the flo# pattern, and not about the flo# speed, isfound. /n order to find flo# velocity indirectly it is necessary to e4pand theanalysis of the #ater property distribution by introducing some physicalprinciples and assumptions. This leads to the geostrophic method.

7.." Requirements to current measurements used in o 'shoreengineering

The large scale circulation can be obtained by indirect methods, but directmeth'ods are necessary for establishing a detailed picture of the flo#. O shoreengineers involved in design and planning of marine structures and operationsneed infor'mation about the current flo# at the sites #here structures are to beinstalled. The long'term distribution of current speed and direction is of course

important, but the variability on short scales in time and space should also beconsidered for deep'#ater fields *see section :.7+.

(p until no# it has been common practice to use averaging periods of :! minutes

and longer #hen recording the current flo# directly. This is su ciently short for

observations of planetary #aves, large eddies, tidal components and other features of

the flo# #hich have return periods in the order of hours, but it is too long for resolving

variations on time scales #hich correspond to dynamic response periods of marine

structures. )uch periods are in the order of seconds or minutes, and this should be

considered #hen planning measurement programs aimed at establishing design

current data for o shore engineering activity in any given deep'#ater field.


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"D CHAPTER @ CURRENT MEASUREMENTS EST O% NORAD

%athiesen *:CCD+ recommended that current flo# data be recorded #ith a

sam'pling frequency of : 6@ close to the sea bed #hen looking for designcriteria for free'spanning pipelines.

Records of salinity and *especially+ temperature can also be very helpful inpro'viding information about the driving mechanisms causing the current flo#,and should be included in the measurement program if possible.

The number of current meters at a site or along a pipeline route must be finite,

and there #ill al#ays be some uncertainty about #hat the flo# field is like

bet#een the current meters. One #ay of reducing this uncertainty #ould be to

install an A$- on an A(=: and have it navigate bet#een the current meters atthe site or along the pipeline route. -urrent data recorded by the A(=Gs A$-

could then be compared to those recorded by the fi4ed current meters, and

transfer functions could be established such as to be able to determine the flo# at

any given location based on readings from the current meters at their fi4ed

locations. A(= technology for use in the o shore industry is being developed, and

a fe# vehicles are currently in use, mainly for seabed mapping and sub'bottom

profiling. A(=s have proven significantly cheaper, faster and easier to use for

these purposes than the conventionally used to#'fish, and these advantages

might be equally applicable to tasks such as pipeline inspection and current

profiling. (p until no#, ho#ever, current measurements using A(=s have mainly

been for purely scientific oceanocraphic studies, see e.g. $hanak et al. *!!:+,

udvigsen et al. *!!7+, )chmidt et al. *:CCD+ and )tansfield et al. *!!:+.

7.7 -urrent measurement sites

O-5A&OR and )/&T52

7 have collected current flo# data on and above the

continental slope outside the coast of %id'&or#ay, see 2igure 7.. The flo#speed measurements #ere carried out in order to obtain design parametersfor sub'sea structures such as pipelines and riser systems in the area. $ue to

a large under#a'ter slide that took place some B!!! years ago, this is an area#ith a rough bottom topography, see 2igure 7.7.

The data collected at the sites marked PO'/G and PO'//G in 2igure 7. #ererecorded using averaging periods of :! and 7! minutes, #hereas the data from

: An autonomous under#ater vehicle *A(=+ is an unmanned submarine #ith its o#n energy

supply and no cable connection to any support vessel. An A(= can be pre'programmed tofollo# a certain route or it can be controlled by acoustic signals.

Oceanographic -ompany in &or#ay. /nternet N ###.oceanor.com

7The 2oundation for )cientific and /ndustrial Research at the &or#egian /nstitute of Tech'

nology *&T6+ *no#N the &or#egian (niversity of )cience and TechnologyN &T&(+. /nternet N###.sintef.no


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@@ ATER MASSES "

BATHYMETRY (m) − ORMEN LANGE45’ 1000

900 800 700

600 500

400

W o E E E

900

o o o o40’ 1000 3 0 3 6 9

65oN 700

OL−I

64oN

1200

1100800

OL−II

35’

63oN

62oN 1100

o

61oN

63 N 1000

30.00’

60oN 900

800

600

700

59oN

25’

40’HF

58oN

20’ 10’ oE 30’

5

20.00’

2igure 7.N L/cati/n /# t)$ cu--$nt m$a0u-$m$nt 0it$0@ Cu--$nt p-/#i*$0 w$-$m$a0u-$J at OLI anJ OLII@ M$a0u-$m$nt0 n$a- t)$ 0$a $J w$-$ /tain$J at t)$ 0p/t J$n/t$J H%@ T)$ Ji0tanc$ $tw$$n OLI anJ OLII i0 app-/&imat$*' ? i*/m$t$-0@

the site marked P62G #ere recorded using a sampling frequency of : 6@.

7." Eater masses

The #ater masses in the area #here the current measurements #ere carried out may

be divided into di erent layers classified by their origin. The vertical strati'fication

e4hibits a three layer structure. )moothed hydrographic profiles *salinity, temperature

and density+, recorded at a nearby section across the continental slope in 2ebruary

and April of year !!!, are sho#n in 2igure 7.". The seasonal pycno'cline at ?! m

depth and a deep pycnocline at about ?!! m depth is clearly seen. A thin surface

layer *∼?! m thick+ of relatively fresh and cold #ater of coastal;shelf origin constitute

the upper mi4ed layer. The thickness of this layer is strongly influenced by the #inds

and displays significant variation from one day to the ne4t and also over the seasons./n the summer this surface layer is normally #armer


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"B CHAPTER @ CURRENT MEASUREMENTS EST O% NORAD

2igure 7.7N S$cti/n /# t)$ St/-$KKa 0*iJ$ a-$a@

than the #ater underneath. 3elo# this #ater is the inflo# of #arm *∼ B/C + and

saline * 7? ppt+ #ater to the &or#egian )ea, i.e. the &orth Atlantic -urrent *seesection ..?+. The lo#er interface of the Atlantic inflo# is located at a #ater depth

bet#een *roughly+ "!! and !! meters. The #ater in the layer belo# the Atlantic

#ater is of Arctic origin and is often referred to as N/-w$Kian S$a A-ctic Int$-m$Jiat$ at$- . This #ater is very cold *Z!@?/C − !@?/C +, but not as saline*∼7".C ppt+ as the Atlantic #ater. At the interface bet#een the Artic #ater and the

Atlantic #ater #e find the deep pychnocline. This is a pronounced density

gradient caused by the di erences in temperature and salinity bet#een the t#o

#ater masses. $etailed descriptions of #ater masses and currents in the &ordic

)eas can be found in 6ansen and Usterhus *!!!+ and Orvik and &iiler *!!+.

7.? -urrent profile measurements.

%easurements of current speed and direction for a number of depths at locations O'

/ and O'// *see 2igure 7.+ #ere recorded. The instrumental set'up and some results

are sho#n in the final report from the measurement campaign, ønseth et al.


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@@ CURRENT PRO%ILE MEASUREMENTS@ "C

0

200

* m +

400

600

$ e p t h

800

1000

1200 0 1 2 3 4 5 6 7 8 9

−1

Temperature */ -+

$ e p t h * m +

0

200

400

600

800

10001200 34.4 34.6 34.8 35 35.2 35.4 35.6

34.2

)alinity *ppt+

0200

* m +

400

$ e p t h 600

800

1000

1200 27 27.2 27.4 27.6 27.8 28 28.2

26.8

$ensity *σ t +

2igure 7."N Sm//t)$J )'J-/K-ap)' c/**$ct$J in %$-ua-' anJ Ap-i* /# '$a- @

*!!:+. The results have been made available to this study, and a brief description of

the instrumental set'up and data recovery at O'/ and O'// is presented in this

section. The main results *mean, ma4, direction of flo#+, an investigation into the

spatial correlation bet#een the flo# in di erent vertical layers and a closer look at

some interesting flo# events are also provided. The description of the instrumentalset'up is largely based on the final report by ønseth et al. *!!:+.


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?! CHAPTER @ CURRENT MEASUREMENTS EST O% NORAD

7.?.: $escription of current profile measurements

ocations and instrumental set'up

The locations of O'/ and O'// can be seen in 2igure 7.. The current metersat O'/a, O'//a and O'//b #ere attached to a vertical mooring line from ananchor on the sea bed to submerged buoyancy elements. At O'/b, thecurrent meter *&ortek A$+ #as attached to a floating buoy. 54act positions of the various current meter moorings are sho#n in Tables 7.: and 7..

2our di erent current meters #ere used.

• R$/ 3roadband A$- *R$'33'A$-+This is a ? k6@ self'contained A$-. Average velocity profileappro4imately ??! meters above the depth at #hich the instrument #asinstalled #as esti'mated every half hour.

• R$/ &arro#band A$- *R$'&3'A$-+

This is a :?! k6@ self'contained A$-. Average velocity profile appro4i'mately !! meters above the depth at #hich the instrument #as installed#as estimated from the results of 7!! pings emitted at second intervalsduring the :! minute averaging period.

• &ortek A$This instrument is an acoustic doppler profiler *A$+, and it #as mountedon a )ea#atch buoy at O'/b. Average velocity profile from " metersdepth to appro4imately B! meters depth #as estimated every hour over a:! minute averaging period.

• R-%' rotor current meters

This instrument measures the current at the position #here it is installed.-urrent speed is measured by counting the number of rotations of arotor, and the direction is obtained by a magnetic compass. )peed anddirection *velocity+ is recorded every : seconds, and the :! minute

vector averaged current velocity is recorded every :! minutes. Thesecurrent meters #ere also equipped #ith thermistors and a device for measuring the salinity of the #ater.

Tables 7.: and 7. contain an overvie# of the depths #here current flo# data

#ere recorded, and of #hich recording device #as used at each specific depth.

T#o current meter moorings #ere used at O'// and three moorings #ere used at

O'/, see 2igures 7.? and 7.D. The distances bet#een the moorings at station O'

/ is !" meters bet#een O'/a and O'/b, and B?! meters bet#een O'/a and

O'/r. %ooring O'//a is ?:? meters a#ay from mooring O'//b. Ee assume that

the main features of the current flo# measured at O'/a, O'/b and O'/r does not


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@@ CURRENT PRO%ILE MEASUREMENTS@ ?:OL−Ia OL−Ib OL−Ir

Seawatch buoy

197 m Nortek ADP

Buoy Buoy

RCM−7 200m RCM−7 200m

RCM−7 300m Buoy RCM−7 300m

RCM−7 400m RCM−7 400m

RCM−7 500m RCM−7 500m

1088 m

RCM−7 750m

700m

RDI−BB−ADCP5 m

RCM−7 1083m

5 m

2igure 7.?N Cu--$nt m$t$- m//-inK0 at OLI 0c)$matic@

OL−IIa OL−IIb

Buoyancy

180 m

RDI−NB−ADCP

RCM−7 200m

RCM−7 300m773 m

775 m

Buoyancy

RDI−BB−ADCP5 m

RCM−7 770m

5 m

2igure 7.DN Cu--$nt m$t$- m//-inK0 at OLII 0c)$matic@

di er significantly. The same assumption is made for the current flo# measured at

O'//a and O'//b. -omparisons of the time traces of flo# velocity logged at 7!!

meter #ater depth at O'//a *R-%'+ and at O'//b *R$'33'A$-+ are sho#n in

2igure 7.. 5ven though it is clear from 2igure 7. that the assumption that there

is little variation of the flo# in the hori@ontal plane #ithin appro4imately


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? CHAPTER @ CURRENT MEASUREMENTS EST O% NORAD

60

OL−IIa

40 OL−IIb

( c m

/ s )

20

s p e e

d

0

Z o n a

l

−20

−40 11/03 11/04 11/05 11/06 11/07 11/08 11/09 11/10

11/02Time (date in 1999)

70

60 OL−IIa

( c m / s )

OL−IIb

50

s p e

e d40

M e r i

d i o n a

l30

20

10

0 11/03 11/04 11/05 11/06 11/07 11/08 11/09 11/10

11/02Time (date in 1999)

2igure 7.N Cu--$nt m$a0u-$m$nt0 #-/m m$t$-0 J$pt) at OLIIa anJ OLII ? m$t$-0 apa-t #-/m $ac)/t)$-@

:!!! meters is not al#ays valid, it #ill still be upheld during the follo#ingstudies of current profiles.

The data recorded at O'/r have been merged #ith the data from O'/a, and#ill from no# on be referred to as data from O'/a.

As #e have already mentioned *section .."+, the hori@ontal flo# velocities inthe ocean are much larger than the vertical flo# velocities #hen large scaleflo#s are considered. Ehen averaging periods of :! and 7! minutes are used,the vertical velocity practically vanishes. The measured current profiles

therefore consist of hori@ontal flo# velocity measurements only.

$ata recovery

The total measurement period at station O'/ ranges from ;:!':CCC until !;:!'

!!!. At station O'// the total measurement period is from 7;:!':CCC until ::;?'

!!:. All current meters listed in Tables 7.: and 7. #ere not in place the #hole

time, and some of them failed to record flo# data during some periods and;or time

instances. 2igures 7.B and 7.C contains an overvie# of the perio

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