Physical Properties of Turbulent Benthic Boundary Layers Generated by Internal Waves

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Physical Properties of Turbulent Benthic Boundary LayersGenerated by Internal Waves

Charles Lemckert1; Jason Antenucci2; Angelo Saggio3; and Jorg Imberger, M.ASCE4

Abstract: Physical properties of active turbulent benthic boundary layers~TBBL! generated by basin scale internal waves were studiewithin a Northern hemisphere thermally stratified lake. A microstructure profiler was used to measure the nature of the turbulencethe TBBLs while a series of thermistor chains were used to monitor the thermal structure of the lake. It was observed that a wind-anticlockwise diurnal-period vertical mode one Kelvin wave generated large scale motions within the water column, and thainteractions between this wave and the sloping lakebed induced TBBLs. A simple model, based on potential energy change and boshearing, was shown to describe the mean TBBL thickness.

DOI: 10.1061/~ASCE!0733-9429~2004!130:1~58!

CE Database subject headings: Turbulent boundary layers; Lakes; Thermal factors; Water quality; Thickness.

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Introduction

When a stratified fluid is forced to flow over a boundary theinduced shear can generate turbulent motions that vertically mthe water adjacent to the bed. Within lakes, coastal seas, aoceans this vertically well-mixed bottom layer is referred to as thturbulent benthic boundary layer~TBBL!. The inertia drivingthese layers may result from various mechanisms including tshoaling of internal waves on a sloping bed, the geometric focuing of internal waves and bottom flowing gravity currents@sum-maries of these driving mechanisms are presented in Garrett et~1993! and Imberger~1994!#. Importantly, TBBLs are natural fea-tures that strongly influence mixing and energy dissipation ratand ultimately water quality.

TBBLs have significantly different properties to that of themain water mass. The momentum associated with TBBLs, whgenerated by shoaling internal waves, is capable of significanenhancing bottom sediment transport and resuspension rates~e.g.,Gloor et al. 1994; Gross et al. 1994; Pierson and Weyhenmey1994; Jahmlich et al. 1998; Stips et al. 1998!. Additionally,TBBLs are also regions of enhanced turbulent velocities and knetic energy dissipation~Dewey and Crawford 1988; Van Harenet al. 1994; Wu¨est et al. 1996; MacIntyre et al. 1999!. Further,since TBBLs can enhance vertical mixing rates on steeply slopinlake beds these layers also have a strong influence on chem

1School of Engineering, Griffith Univ. Gold Coast Campus,PMB50, Gold Coast Mail Centre, Queensland 9726, Australia. [email protected]

2Centre for Water Research, Univ. of Western Australia, NedlandW.A. 6217, Australia.

3Present Address: Alameda das Rosas, 295, Sao Carlos,13566-560, Brazil. E-mail: [email protected]

4Centre for Water Research, Univ. of Western Australia, NedlandW.A. 6217, Australia.

Note. Discussion open until June 1, 2004. Separate discussions mbe submitted for individual papers. To extend the closing date by onmonth, a written request must be filed with the ASCE Managing EditoThe manuscript for this paper was submitted for review and possibpublication on June 8, 2000; approved on April 23, 2003. This paperpart of theJournal of Hydraulic Engineering, Vol. 130, No. 1, January1, 2004. ©ASCE, ISSN 0733-9429/2004/1-58–69/$18.00.

58 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2004

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and biological processes in lakes~e.g., Wuest et al. 1994; MacIn-tyre et al. 1999; Gloor et al. 2000!. Therefore, it is important thata detailed knowledge of the TBBL dynamics is developed so ththe properties of lake mixing can be better predicted and modele

The thickness of TBBLs has been found to vary dramaticallover sloping boundaries within both lakes and oceans. As noteby Lentz and Trowbridge~1991! the thickness of a TBBL is likelyto be a function of the background stratification, Coriolis acceleration, current magnitude and direction, isopycnal slope, and bslope. In addition to these we would also expect bottom roughness to play a role as this will have an influence on the magnitudof turbulent activity. Stips et al.~1998!, in an extensive study ofboundary layers within shallow seas, found that the TBBL layethickness~which they refer to as the homogeneous layer thickness! was independent of the local mean layer velocity and turbulent kinetic energy dissipation rates, and that existing modecould not predict its thickness. Interestingly, they found that thlayer thickness was best correlated to the wind speed averagover two days. Shorter period averaging had no correlation, rvealing that the adjustment time of the layer was zero~two days!;implying that large scale motions dominate the layer propertieThey concluded that the mixing processes responsible for thlayer thickness must have taken place elsewhere and at an eartime, with the layer water being advected into the region.

Gloor et al.~2000! found that within a thermally stratified lakesubjected to an intermittent two-dimensional standing internal siches ~periods ;0.5 and 1 day! the TBBL developed rapidly~;1–3 h! on the sloping boundaries of the lake with the layethickness varying markedly with time and space. For periods ohigh stratification and relatively weak internal seiche activity theTBBL did not develop. When wind conditions were sufficientlyenergetic a TBBL developed, with the layer thickness increasinlinearly with the inverse of the density gradient. Following thecessation of seiche activity the TBBL thickness decayed at a radepending upon location and level of background stratificationOn the steeply sloping boundaries of the lake~slope;0.02! thiswas rapid due to the formation of intrusion events that carried thmixed water of the TBBL into the interior. For the near horizontabed regions, the reduction was significantly reduced since verticdiffusion was the dominant decay mechanism. Using simple e

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ergy considerations, vertical diffusion and intrusion dynamicthey were able to derive and test a simple model for predicting thTBBL layer thickness for their studied conditions. They foundthat the model worked well for their intermittent two-dimensionaconditions when the water column temperature structure and tflow within the TBBL were well documented.

This paper presents the findings obtained from two field stuies, performed on Lake Kinneret, Israel, which is a large lake thexperiences strong thermal stratification and wind forcing evenData presented in this paper were collected using thermistchains, acoustic Doppler flow meters, and a microstructure prfiler capable of measuring temperature, conductivity, and veloci~vertically at 1 mm intervals!. Time series data from the ther-mistor chains and current meters were used to determine theture of basin scale oscillations that energized a TBBL, while thmicrostructure data were used to describe some of the meTBBL properties. Methods for determining the bottom drag coeficient and predicting the TBBL thickness for a three-dimensionawave field are presented and discussed. It was found thatmean TBBL thickness is a function of the background stratifica

Fig. 1. Bathymetric map of Lake Kinneret showing locations ofthermistor chains~indicated by T#! and 1996 acoustic flow meter site~N!. Numbers between parentheses correspond to phase relative toof 24 h period Kelvin wave. Phases were computed from displacment of the 20°C isotherm and all values shown have confidenhigher than 95% level.

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tion, the bottom shear velocity, and the age of the layer. Imptantly, the TBBL thickness, at any location and time, also depeon the phases of the three-dimensional basin scale oscillatthat generated the layer.

Experimental Methodology

Data used in this investigation were collected during two sepafield programs conducted within Lake Kinneret, Israel~see Fig.1!. The first study was performed from June 29 to July 12, 19while the second was performed from June 10 to July 6, 19This large freshwater lake has a surface area of 168 km2, a meandepth of 24 m, and a maximum depth of 42 m. From AprilDecember the lake is thermally stratified, with wind stirred sface water~epilimnion—see Fig. 2! overlying slightly stratifiedbottom water~hypolimnion! that are separated by a zone of higtemperature gradients~metalimnion!. The average metalimniondepth of approximately 15 m~e.g., Serruya 1975; Shteinmaet al. 1997!. Strong periodic winds~usually westerly! result in thegeneration of large-scale metalimnion displacements, withdominant periods of 24 and 12 h. These have been shown tbasin-scale Kelvin and Poincare waves of the first vertical mo~Ou and Bennett 1979; Antenucci et al. 2000!. Lemckert and Im-berger~1998! showed that these basin-scale oscillations were ato generate TBBLs that were capable of inducing active vertimixing and mass transport.

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Fig. 2. Vertical profiles of~a! temperature and~b! gradient tempera-ture recorded during transect across portion of Lake Kinneret on175, 1997. The text mhp #### indicates that data were collectedPFP at #### hours~local time!. TBBL can be clearly seen as neaconstant temperature bottom layer and with strong temperaturedients also marking its upper level. Times in hours for each proare given in~a!.

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Table 1. Depth of Temperature Sensors~in m! used on Thermistor Chains during 1996 and 1997 Lake Kinneret Experiments. Bracketed NumbIndicate Sampling Period

Thermistor chain number and corresponding sampling rate

1996 1997

T1~15 s!

T2~15 s!

T3~15 s!

T1~300 s!

T2~10 s!

T3~10 s!

T4~300 s!

T5~20 s!

T6~10 s!

T7~300 s!

T9~300 s!

1 1 1 1 1 1 1 4 1 1 15 3 3 4 4 4 4 6 4 4 4

10 5 5 6 6 6 6 8.6 6 6 612.5 6.5 6.5 7 7 8 8 11.2 7 7 714 8 8 8 8 9 9 13.8 8 8 815 9 9 9 9 10 10 16.4 9 9 916 10 10 10 10 11 11 19 10 10 1017 11 11 11 11 12 12 20 11 11 1118 12 12 12 12 13 13 22 12 12 1219 13 13 13 13 14 14 24 13 13 1320 14 14 14 14 15 15 26 14 14 1421 15 15 14.5 14.5 16 16 27 14.5 14.5 14.522 16 16 15 15 17 17 — 15 15 1523 17 17 16 16 18 18 — 16 16 1624 18 18 17 17 19 19 — 17 17 1725 19 19 18 18 20 20 — 18 18 1826 20 20 19 19 22 22 — 19 19 1927 21 21 20 20 25 25 — 20 20 2028 22 22 21 21 29 32 — 21 21 2130 22.5 22.5 22 22 33 40 — 22 22 22

22 22 33 40 — 22 22 22

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Continuous records of the thermal structure within Lake Kneret were recorded using a series of thermistor chains positioaround the lake. Each chain consisted of a series of fast respthermistors, with accuracies of 0.01°C, which were calibratedmediately before and checked again after each deployment.depth of the thermistors and the rate at which they were samare listed in Table 1, while the corresponding deployment lotions are displayed in Fig. 1. Time series of the isotherm positiwere derived from linear interpolation of the temperature recorTable 2 summarizes the time periods over which data werelected from the various instruments and chains.

In 1996, two identical single-beam acoustic Doppler curreprofilers~ADCPs! ~Bugnon and Whitehouse 1991! were deployednear Site T2 at a depth of 21 m. These 1,200 kHz instrumewere placed normal to each other, aligned at north-south~N-S!and east-west~E-W!, and the beams set at an angle of 70° to thorizontal. By assuming that the water flow was predominanparallel to the bed the combined signals from these instrumewere used to resolve the boundary flows 1–7 m above thebed. The ADCPs were configured to sample the water columhourly intervals, have vertical spatial resolutions of 0.3 m, avelocity resolutions of 2% of the actual flow velocity. These istruments were checked for correct operation both immediabefore and after the field trips.

Vertical profiles of temperature, temperature gradient, condtivity, and velocity within Lake Kinneret were recorded at varioutimes and locations using the Portable Flux Profiler~PFP! ~Im-berger and Head 1994; Lemckert and Imberger 1998!. During the1996 experiment this battery-powered profiler was released at


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Table 2. Deployment Periods of Various Instruments used duringStudy of Turbulent Benthic Boundary Layer in 1996 and 1997 LakeKinneret Experiments. Days for Portable Flux Profiler Usage arethose from which Useful Turbulent Benthic Boundary Layer DataCould be Derived~According to Previously Defined Constraints onData!

Thermistor chains ~Day number of the year!

1996T1 From 165 to 178T2 From 166 to 178T3 From 165 to 178

173/175Acoustic Dopplercurrent profiler

From 164 to 177

1997T1 From 166 to 182T2 From 165 to 182T3 From 164 to 182T4 From 165 to 182T5 From 166 to 177T6 From 166 to 177T7 From 163 to 182T8 —T9 From 164 to 182

171/174/175/180/181Acoustic Dopplercurrent profilers~ADCPs!

ADCP-1 from 167 to 172and from 174 to 182

ADCP-2 from 168 to 181

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surface, and allowed to free fall to the bed at a nominal rate ofm21. Protruding from the front of the probe were the sensincomponents of a two-component laser Doppler velocime~LDV ! system and two combined four-electrode conductivittemperature sensors. The probe was also equipped with a pressensor,x-y tilt sensors and a compass for measuring probe depinclination, and orientation, respectively. The LDV, which hadvelocity resolution of 1.231023 ms21, measured the vertical andone horizontal component of the water velocity~relative to theprobe! 3 mm above a temperature/conductivity sensor pair. Tcompass and tilt sensors had resolutions of 3° and 0.1°, resptively while the resolutions of the temperature, conductivity, anpressure sensors were 631024°C, 231024 Sm21, and 231023 m, respectively. A sensor guard protruding from the froof the probe ensured that the sensors did not strike the bed. Hever, this guard, which was designed not to influence the flowwater past the sensors, resulted in profiling ceasing 0.1 m frthe lakebed. Data from the temperature and conductivity senswere sharpened and smoothed digitally to match sensor respofunctions so that salinity and density spiking occurrences, resing from sensor response mismatching, were avoided~Fozdaret al. 1985!. To ensure accuracy and correct performance, the Pwas calibrated immediately before the experiments and checimmediately afterwards.

In the 1997 study an additional LDV system was added to tportable flux profiler. The new system was positioned normalthe existing LDV system; thus allowing for the measurementall three components of velocity relative to the probe. With thnew LDV arrangement it was possible to estimate the water cumn flow velocities~relative to the bed! through the integration ofthe drag force on the probe as it freely falls. As the PFP dscended through the water column it recorded velocity data retive to itself. To determine the water velocities of the water coumn relative to the bed PFP horizontal velocity measuremewere decomposed into N-S and W-E components and then usecalculate the dragFd on the probe in each of these directions b

Fd50.5CdrUPuUPu (1)

where Cd5drag coefficient due to horizontal flow componentr5water density; andUP5horizontal velocity vector. The com-ponents of the horizontal flow velocity relative to the bedUB

were then estimated by integratingFd from the bottom to the topof the profile using

UBn115UBn

1Fd

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whereDt5sampling rate of the probe~100 Hz!; M5probes mass;and the subscriptn denoted the integral step. It was assumed thUB050 ms21, even though it is recognized that the LDV sensinvolume did not quite reach the bed. Fig. 3, using data collecduring a 1998 experiment on Lake Kinneret, compares an ADderived profile with that determined using the LDV system of thPFP and the model described by Eq.~2!. In this 1998 experimentthe ADCP was deployed by suspending it from a chain, at 22depth ~pointing upwards!. The presented data shows that thmodel quite successfully reproduced the actual water columnlocity profile. The observed differences are expected to beconsequence of variations in sampling rates and slightly differsampling locations. The presented PFP profile was derived frdata collected 100 m from the ADCP deployment site.

The turbulent properties of mixing events within stratifieshear flows are often characterized using dimensionless raThe two most common are the turbulent Froude and Reyno

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numbers~e.g., Gibson 1980; Ivey and Imberger 1991!. In a simi-lar manner to the common large scale Froude and Reynolds num-bers these turbulence based quantities respectively represent abalance between turbulent inertia and buoyancy, and turbulentinertia and viscous damping over a defined turbulent length scale.They are, respectively, defined by

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whereu85(«LC)1/35RMS turbulent velocity scale of the event~Ivey and Imberger 1991!; «5rate of dissipation of turbulent ki-netic energy;Lc5statistical average measure of the vertical lengthscale of the energy bearing eddies within the event~Imberger andBoashash 1986!; N52(g/r)(dr/dz)1/25buoyancy frequency;g5acceleration due to gravity;r5fluid density; andz5elevation;LO5(«/N3)1/25Ozmidov length scale, which represents the larg-est possible overturn length for a given« and backgroundN ~e.g.Gibson 1980!; n5viscosity; and LK5(n3/«)1/45Kolmogorovlength scale, which represents the smallest scale of active turbu-lence~e.g., Gibson 1980!. The length scaleLc is obtained by firstcalculating the distance a fluid element has been displaced fromits level of neutral buoyancy in a monotonized profile~this dis-tance is referred to as the Thorpe displacement scaleLd). Follow-ing this, the displacement estimatesLd are moved vertically byone half of their value, thereby placing them at the center of theoverturn event. The absolute values of all the estimates at a par-ticular depth are then summed and averaged at their new position;giving a measure of the eddy displacementLc , which is nowpositioned at the event center. WhenFt is large~.1! inertia domi-nates over the buoyancy restoring force, while forFt,1 turbulent

Fig. 3. Comparison of water velocities derived from ADCP and PFPduring a trial experiment. Components shown are~a! N-S and ~b!E-W. In this example PFP derived estimates were collected over pe-riod of 80 s as instrument descended from 14 to 22 m, while ADCPestimates were derived from data collected over a period of 600 s.Feature shown between 14 and 21 m is due to higher vertical modePoincare waves~Antenucci et al. 2000!.

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is anisotropic. ForRt,15 viscosity dampens inertia and turbulenevents are unable to induce active mixing.

Ft andRt must be determined from sections of profile data thaare statistically stationary. In this study stationarity was detemined using the segmentation processes detailed in Imberger aIvey ~1991!. Briefly, the process involves fitting a fourth-orderautoregressive model to the measured temperature gradient sigdata over two adjacent windows of equal size and using the rsultant pair of model coefficients to assess the difference betwewindows, with large differences indicating a nonstationary relationship. The window pair is moved through a profile on a pointto-point basis; the statistical difference is then measured by coputing the derivative of the distance function. By selectingderivative threshold, stationary regions can be defined as thoareas contained wholly within high thresholds.

The upper limits of the TBBLs were marked by sharp changein temperature gradient as the near homogeneous TBBL wainteracted with the stratified interior lake water~e.g., see Fig. 2!.The height of the TBBLs,h, was therefore set to be the heightabove the bed of the upper limit of the bottom stationary segmeIf the stationarity test resulted in an apparent temperature homgeneous TBBL being divided into more than one stationary sement, that data was not used for further processing. As a conquence of these constraints less than 30% of the casts performproduced suitable TBBL data. This means that we were limitedinvestigating mean TBBL properties since there was insufficiedata to gain statistical significance of point-by-point profile properties.

In order to estimate the turbulent velocity fluctuationsu8, v8,andw8, which are necessary for determining various TBBL properties, a low pass variable length filter was applied over the mesured PFP recorded velocities. This gave the nonturbulent partthe signal which was then subtracted from the measured veloties, resulting in profile estimates ofu8, v8, andw8. The variablefilter consisted of a nonrecursive Gaussian filter with a standadeviation equal to the value of the envelope ofLc in the profile~Saggio and Imberger 2001!. The envelope ofLc was defined asthe maximum ofLc over a window of lengthLc ~a low pass 25Hz cutoff frequency was firstly applied toLc to remove spikes inthe signal!. The nonrecursive nature of the filter avoided problemlike rippling and phase shift in the signal at the expense of largcomputational effort. The definition of the envelope ofLc as thestandard deviation of the Gaussian filter, ensured that all the tubulent fluctuations of scales shorter than the maximumLc in apatch were left in the profile data.

While u8 could be determined using velocity data collected bthe profiler, LDV noise levels limited the range over whichu8,and consequently«, could be accurately determined. For exampleLemckert and Imberger~1998! found that LDV determined dissi-pation estimates «LDV were only valid when «LDV

.1028 m2 s23; however, for this study, significantly lower valueswere expected. Consequently, the dissipation rates within statioary segments were determined using a Batchelor curve-fittintechnique applied to the temperature gradient signals. This pmitted « to be determined down to 10210m2 s23 with an error of,10% ~Luketina and Imberger 2001!. Further, data within thestationary segment were only used if it was free of any large noispikes induced by underwater objects that had a marked spurioinfluence on the LDV signals, and if the conditionLS /Lc.2,whereLS is the segment length, was satisfied. This latter restraiensured that we actually captured complete events and not a ption thereof.


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Discussion

Large Scale Conditions

The wind pattern recorded during both study programs was domi-nated by a strong diurnal cycle with calm morning conditions andstrong westerly winds that reached 10 ms21 commencing in theearly afternoon@see Figs. 4~a! and 5~a!#. A section of the iso-therms derived from thermistor chain data collected during the1996 experiment is presented in Fig. 4~b!. Here, the metalimnionisotherms underwent significant vertical oscillations and associ-ated strong near boundary flows. The 1997 data also showed thecontinual existence of the large-scale metalimnion oscillations,with two main forms dominating@see Fig. 5~b!#. The first was thatof a 24 h oscillation, while the second was that of a lower ampli-tude, 12 h oscillation. Spectral estimates were derived for thewind and the 20°C isotherm displacements derived from ChainT2, which was chosen as it characterized the metalimnion behav-ior. The results, presented in Fig. 6, show a strong correlationbetween the wind and the observed isotherm oscillations. Themost energetic metalimnion oscillation had a period of 24 h~fre-quency of 1.1631025 Hz) while the second most energetic was12 h ~frequency of 2.3131025 Hz). The high correlation betweenthe wind and isotherm signals reveals that the wind field wasdriving the two dominant metalimnion oscillations.

Using the 1997 data, phase estimations were calculated be-tween thermistor chain data sets to determine the nature of thedominant 24 h oscillation. The estimations of phase difference arepresented in Fig. 1. They reveal that the predominant 24 h fluc-tuation is linked to a basin-scale wave rotating around the lake ina counterclockwise direction. This wave was first identified as aKelvin wave of the first vertical mode by Ou and Bennett~1979!.Kelvin waves are sinusoidal shaped waves that are trapped on andpropagates along the sloping sides of a stratified lake or ocean.The spatial structure of the wave, and response of the wave toseasonal forcing conditions, were described by Antenucci et al.~2000!. The offshore decay of the wave amplitude was found tobe almost linear, as the internal Rossby radius was of similar scaleto the basin width. The Kelvin wave was measurable in all re-gions of the lake, but was stronger in the boundaries due to thedecrease in depth. This Kelvin wave activity resulted in the de-velopment of significant long-slope velocities and mass transport~see Fig. 4! with the highest velocities occurring at the node of themetalimnion oscillations.

The shorter 12 h oscillations were identified by Antenucciet al.~2000! as a Poincare wave of the first horizontal and verticalmode. The wave is progressive, with the phase propagating clock-wise around the basin. Along the western shore, Antenucci et al.~2000! showed that the metalimnion response was due to both theKelvin and Poincare waves. The crests of the Poincare waveoccur in Fig. 5 daily around 8 a.m., in the trough of the Kelvinwave. The second crest of the Poincare wave was occurring at thesame time as the crest of the Kelvin wave.

Properties of the Turbulent Benthic Boundary Layer

In this work, as is generally accepted, TBBLs are defined as beingthose regions adjacent to the bed where turbulent activity keepsthe vertical density structure nearly constant~e.g., Trowbridgeand Lentz 1991; Gloor et al. 1994; Lemckert and Imberger 1998!.Fig. 2 shows how the top of the TBBL is characterized by strongtemperature gradients that lead to rapid temperature changes. Fig.2~a! also reveals how a near thermally homogeneous TBBL ex-

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Fig. 4. ~Color! ~a! Wind velocities~E-W and N-S components!, and color contour plots of~b! near bottom water velocities speed and~c! directionas measured using the ADCPs on Day 175, 1996. The ADCP was deployed on bed at depth of 21 m near site T2. Bottom 1 m ofdata is missingdue to transducer ring down and deployment height of ADCPs. Solid lines are derived isotherms~in °C! from Station T2.

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isted within Lake Kinneret and that its thickness decreasedslope, while the background stratification decreased down-sloat the time of sampling on Day 175~June 24!, 1997. While thisfigure was derived from data collected over a four-hour perithis time scale is significantly smaller than the dominant bastime scale of 24 h~Fig. 6!.

Fig. 7 presents an example of a PFP cast undertaken in 19Here it is seen that the 1.8 m thick TBBL is nearly homogeneowith a strong temperature gradient marking its upper limit wi

Fig. 5. ~a! Wind velocities and~b! isotherms~in °C! derived fromThermistor Chain T2 from data collected during portion of 199experiment

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the velocity profile data showing significant speed oscillations.These oscillations, along with the high dissipation rate estimate ofthe stationary TBBL bottom layer segment, indicate active mix-ing. Figs. 7~h, i, and j! display an example of the estimated fluc-tuating velocity components derived using the above-mentionedfilter. These results show that within the TBBL there were signifi-

Fig. 6. Power spectral density estimates of wind speed and 20°Cisotherm for data collected between days of year 171 and 181, 1997~corresponding to data presented in Fig. 4!. For coherency plot, solidline shows magnitude-squared coherence, dashed line shows limit ofsignificance coherence for 95% confidence, and stars represent phasdifference between signals.


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Fig. 7. Example of microstructure data collected and derived from PFP cast performed during 1997 Lake Kinneret experiment at 0910 h180. Data presented are~a! temperature,~b! s t(5r21,000), ~c! dT/dz, ~d! horizontal water speed relative to bed,~e! flow direction, ~f!temperature,~g! segment averaged estimates of«, ~h! u8, ~i! w8, and~j! u8w8. TBBL, which extends down from 17.7 m, was found to be onstatistically stationary segment~using the method of Imberger and Ivey 1991!.


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Fig. 8. Typical example of velocity spectrum of~a! u8, ~b! w8, and~c! corresponding cospectrum derived from PFP data collected withTBBL. Data presented corresponds to bottom segment of Fig. 4. 95confidence intervals are shown. Roll off observed in spectra are resof filter applied to raw LDV signals to remove any high frequencynoise. Note thatv signal has very similar noise properties tou andw.

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J. Hydraul. Eng. 20

cant turbulent velocities in all three components that were weabove the noise level of the LDV system. The velocity fluctuations, and their product, rapidly decrease at the top of the TBBLindicating that stratification effects are influencing the layer dynamics. Fig. 8 presents the velocity spectral estimates, and tcorresponding co-spectrum for the TBBL segment. These resuclearly show that for the TBBL the flow was turbulent and thathe PFP noise level is well below that necessary to determinestimates of Reynolds stress, which is necessary for determinibottom drag coefficients.

Fig. 9 presents a time history of the layer thickness and turbulent properties of a TBBL recorded near Site T2 during the 199experiment. The layer thickness was found to change as a funtion of time. The decrease inh after 1,000 h corresponded to thePoincare wave crest moving away from the site. The rapid increase inh after 1,400 h corresponded to the crests of the Kelviand Poincare waves approaching the site The derived valuesthe turbulentFt and Rt @Figs. 9~c and d!, respectively# indicatethat the observed TBBL was an active mixing zone capable oinducing vertical mass transport~Ivey and Imberger 1991; Lem-ckert and Imberger 1998!.

When considering only the 1996 data, Fig. 10 shows that theis a distinct change in TBBL turbulent properties ath51.3 m(5hcrit). However, in 1997 a distinct change can be observedoccur ath51.8 m(5hcrit). As will be discussed later, this differ-ence in critical values may be linked to the degree of stratification, TBBL layer development time, the internal wave energy anthe phases of the waves at the time of recording the data.

In both studies it was found that whenh,hcrit data were col-lected in the region of the metalimnion~i.e., strong stratification!as it directly interacted with the lake bed. There was an observe

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Fig. 9. Plots of change in~a! TBBL layer thicknessh, and~b! «, ~c!Ft and ~d! Rt as function of time as derived from PFP profile datacollected on Day 175, 1996, near Site T2. The changing thicknessTBBL is primarily due to phase of Kelvin and Poincare waves.

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increase in« with h, which was the result of a general increase inthe mean TBBL layer velocity@see Fig. 10~a! when h,hcrit] .Therefore, the TBBL was found to exist in a region of high background density gradients, which inhibited active growth as somof the TBBL energy would have to go into mixing the stratifiedfluid. A similar result was found in the ocean study of Houghton~1995! who concluded that a stratified layer could significantlyinhibit the growth of a benthic boundary layer. Examination of theFt andRt shows that with reducingh stratification and viscosityboth play an important role in inhibiting active turbulence withinthe TBBL. This is also in part due to the reduction in mean TBBLvelocity.

Whenh.hcrit the TBBL was usually sampled at greater depthsaway from the metalimnion/bed interaction zone, where the ambient density gradients were significantly reduced. Within this region, the TBBL depth averaged« was found to decrease withincreasingh and depth~see Fig. 11! even though the mean layervelocities were observed to have no general trend@see Fig. 10~a!#.The values ofFt andRt show that in this region the TBBL is stillcapable of active vertical mixing.

Prediction of the Turbulent Benthic Boundary LayerThickness

In this study, there were insufficient data collected to use correlation techniques to determine functional dependencies of thTBBL thickness on external factors, such as Coriolis effects

Fig. 10. Plots of mean TBBL layer velocity as determined with PFPU, ~b! «, ~c! Ft and ~d! Rt as function ofh. Data presented werecollected duringn 1996 and d 1997 experiments. N.B. forh,1.5 m in 1996 and forh,2 m in 1997 stratification dominates flowdynamics.


J. Hydraul. Eng. 200

owever, similar to Gloor et al.~2000! it is possible to use simplessumptions to develop a layer thickness prediction model fo

hree-dimensional type wave field. Consider now that the thicning of the TBBL, and hence its change in potential eneralances the shearing energy resulting from flow/bed interacti

hen, following Fischer et al.~1979!, it can be shown

1

2

Dr

rgh

dh

dt5

1

2Ck* u* 3 (5)

hereCk* '0.235measure of the efficiency of energy utilizatioFischer et al. 1979! and t5time. If it is considered that the den-ity gradient is linear, so thatgDr/r51/2N2h, and the shearelocity u* is due to the basin scale wave motions such thatu*um* sinÃt, wherev is the wave frequency andum* is the maxi-um absolute value, then Eq.~5! can then be written as

h2dh

dt5

2Ck* ~um* sinÃt !3

N2(6)

n the work of Gloor et al.~2000! they had direct measures of thurrents within the TBBL for the duration of TBBL formation;O (days)# and decay. Consequently, they were not requiredredict the cyclic behavior of the bed velocity Eq.~6!. Therefore,

he term 2Ck* (um* sinvt)3 was presented as 4gmixchuuu3 wheremix is the fraction of the kinetic energy that is convertedotential energy~estimated to be 0.01!, Ck* is the bottom dragoefficient, andu is the TBBL velocity.

For Lake Kinneret, which was subjected to persistent bacale internal waves, Eq.~6! can be integrated with respect toime over one half wave period to give

hi 113 5hi

318Ck* um*

3

N2Ã(7)

here the subscripti denotes the number of half wave periodollowing the initiation of the wave motion, which begins aproximately when the lake becomes stratified and the strongrnal wind cycle commences. Eq.~7! shows how, through en-

rainment, the mean layer thickness will grow at any onarticular point within the lake, with the background stratificatioindering that growth. That is, in areas of high stratification, sus occurs in the metalimnion, the TBBL would be thinner tha

hat of the weakly stratified hypolimnion region, for the samegree ofum* .

ig. 11. Plot of segment averaged« as function of depth for dataollected during 1997 experiment

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For the present data set, and since we did not have appropriadirect continual bottom current measurements, the TBBL segmenaveraged estimates ofu8w8 and v8w8 were used to derive theTBBL averaged Reynolds stress and ultimately the average TBBshear velocity from:

u* 5S tL

rLD 1/2

(8)

where tL5rL(u8w821v8w82)1/25average TBBL shear stress;rL5average TBBL density;u8w8 and v8w85Reynolds stresscomponents, with the overbars indicating that the values weraveraged over the entire TBBL. This method was also used bDallimore et al.~2001! and Saggio and Imberger~2001!.

Within Lake Kinneret the persistence of the TBBL was theresult of the continual internal wave activity and if no water werelost from the TBBL then it would continue to grow unabated. If itis assumed that the dominant loss of water from the TBBL wasthe result of vertical diffusion than the rate of decay inh withtime can be shown to be~following Gloor et al. 2000!

dh

dt52

K

h(9)

where K5vertical diffusion coefficient, which in keeping withGloor et al.~2000! we will assume here to be;331026.

In 1997 it was possible to use the PFP data to estimate thvalues necessary to apply Eqs.~7! and ~9! in order to find themean TBBL layer thickness. In this year the lake became stratified on Day 120. Assuming that the stratification within the watercolumn increases linearly with time and thatum* was constant at531023 ms21 ~maximum recorded value!, then it was possible toderive the theoretical maximum layer thickness for various levelsof stratification, which in turn corresponded to different lakedepths. Results from this model, and the actual recorded value~derived from chain and profile data!, are presented in Table 3.There is excellent agreement between the theoretical and expementally derived results, indicating that the simple model is aneffective predictive tool.

The model presented above and the experimental findingtherefore indicate that the mean TBBL layer thickness is a function of age, background stratification, location, and internal waveenergy, as the latter drives the bottom shear flows. It is importanto remember that as the result of isotherm oscillations induced bwave internal motions~which can also result in convergent ordivergent behavior on the sloping boundary! the instantaneousTBBL thickness at any one location will vary with time~as shownin Fig. 8!.

Behavior of Bottom Drag Coefficient

From segment averaged TBBL speedU andu* it was possible toestimate a TBBL depth averaged drag coefficientCD which, bydefinition, is given by

Table 3. Comparison of Measured and Predicted Turbulent BenthicBoundary Layer Thicknesses Assuming there were Approximately 60Days of Layer Development Time

DescriptionN

(31023 rads21)Measuredh

~m!Predictedh

~m!

Base of epilimnion — Not found —Midmetalimnion 31 4 3.8Upper hypolimnion 15 6 6.6Middeep hypolimnion 8 10 10.3

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J. Hydraul. Eng. 20

et

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i-

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CD5u* 2

U2(10)

Using the available data from 1997 the average value oCD

was found to be 0.0035~from 28 values, standard deviati50.003!. The magnitude of this result is in keeping with thoseLentz and Trowbridge~1991!, Trowbridge and Lentz~1991,1998! and Cheng et al.~1999! who all used moored curremeters and bottom log-profile methods to estimate bottom swith the latter writers finding values ranging between 0.00210.0064~in an estuarine channel!. Dewey and Crawford~1988!, inanother oceanic study of TBBLs used moored current metera profiling microstructure velocity profiler to estimate dissiparates and derived a meanCD of 0.6931023 with a meanR esti-mated to beO (105).

The derivation ofCD in this study is based upon segmeaveraged values. Dewey and Crawford~1988! employed twomethods to estimateCD . One method determined shear velociassuming a constant shear layer~CSL! that exists adjacent to thbed where the Reynolds stress is constant over a layer. Usinassumption they derived the shear velocity fromU5u* /K(ln z/d)1du*2/y, whereK50.4 is the von Karman constant andd is a length scale proportional to the height ofviscous sublayer. The second method assumed that in the bboundary layer there is likely to be a local balance betweenrate of production of turbulent kinetic energy, through the Rnolds stress working on the mean shear, and the rate of vidissipation of that energy. From this the shear velocity wasrived from data collected at a fixed altitudez in the CSL using«5ru* 3/Kz. In lakes TBBLs are typicallyO (1 m), while in theocean they are typicallyO (10 m). For the methodologies usedthis investigation it was not possible to accurately resolve thewithin the CSL. Consequently, it was necessary to determinCD

using the TBBL averaged values.

Conclusion

Measurements of the thermal structure within Lake Kinnerevealed a 24 h period Kelvin wave and a 12 h period Poinwave, as previously observed in the lake. These large-scaleforced internal wave oscillations were observed to have suffienergy to generate and maintain an active turbulent beboundary layer. The thickness of this layer, as derived froprofiling microstructure instrument, was found to vary longcross slope depending upon the sampling location and theof the internal wave field. Data from the profiling instrument aled to an estimate of the bottom drag coefficient, indicatingsuitable designed profiling devices have the potential to assestimating larger scale lake properties and that moored de~such as current meter arrays! may not always be required.

The turbulent properties of the TBBLs were found to berectly related to the TBBL layer thickness, which was in tdependent upon the degree of stratification adjacent to thebed. It was determined that the TBBL layer could be charaized as a shear driven layer which therefore led to the devment of a simple model, based on potential energy changeboundary shearing, that was shown to describe the mean Tthickness. The model assumes that the average TBBL thickncontrolled predominately by vertical processes.

Acknowledgments

This project was partially supported by funds from the AustraResearch Council~ARC! Large Grant Scheme~Grant No.

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A89531551!, the Department of Industry, Science and Technol-ogy, Bilateral Collaboration Program, the Center for Water Re-search, University of Western Australia, the School of Engineer-ing and Technology, Deakin University, Australia, and the Schoolof Engineering, Griffith University Gold Coast Campus, Austra-lia. This study could not have been carried out without the excel-lent assistance and facilities~including the use of their thermistorchain data from chain T5! of the Y. Alon Kinneret LimnologicalLaboratory, Israel Oceanographic and Limnological ResearchLtd., and the active and generous support by many of its staffmembers. The writers would like to thank David Luketina, Caro-lyn Oldham, and anonymous reviewers for comments made onearlier versions of this manuscript.

Notation

The following symbols are used in this paper:Cd 5 probe drag coefficient due to horizontal flow components;Ck* 5 measure of efficiency of energy utilization;Fd 5 horizontal drag force on probe;Ft 5 turbulent Froude number;h 5 TBBL thickness;

Ld 5 Thorpe length scale;Lc 5 statistical average measure of vertical length scale of

energy bearing eddies;LK 5 Kolmogorov length scale;LO 5 Ozmidov length scale;M 5 probes mass;N 5 buoyancy frequency;

Rt 5 turbulent Reynolds number;t 5 time;

UB 5 t horizontal flow velocity relative to bed;UP 5 horizontal velocity vector;u8 5 RMS turbulent velocity scale;u* 5 shear velocity;um* 5 maximum shear velocity;Dt 5 sampling rate of probe;

« 5 rate of dissipation of turbulent kinetic energy;n 5 viscosity;r 5 density; andv 5 wave frequency.

Subscriptsi 5 time step; andn 5 integral step.

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Physical Properties of Turbulent Benthic Boundary Layers Generated by Internal Waves

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