Comparison of dissipation of turbulent kinetic energy determined from shear and temperature microstructure

Kocsis, Otti; Prandke, Hartmut; Adolf, Stips; Simon, André Louis; Wüest, Alfred

doi:10.1016/s0924-7963(99)00006-8

Cited by 84 publications

(74 citation statements)

References 30 publications

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“…In addition, our interior estimates (between 10 Ϫ9 and 10 Ϫ10 W kg Ϫ1 ) are consistent with offshore Mono Lake thermocline data (MacIntyre et al 1999), interior (below 10 m) Lake Alpnach data (Wüest et al 1996), and Lake Constance data under low wind forcing (Kocsis et al 1998). Finally, the average dissipation ⑀ ϳ 10 Ϫ10 W kg Ϫ1 in a stratification of N 2 ϳ 2 ϫ 10 Ϫ8 s Ϫ2 implies active-or even isotropicturbulence (⑀ ϳ 100 ϫ (25N 2 ); Gargett et al 1984) with huge overturning eddies (Ozmidov scale (⑀N Ϫ3 ) 1/2 ϳ 5 m).…”

Section: ϫ10supporting

confidence: 88%

“…Temperature spectra, calculated from the 2 m long vertical segments, which did not follow Batchelor's form (less than 10% of the spectra) were rejected and not analyzed further. With this arrangement, dissipation ⑀ (when between 10 Ϫ12 and 7 ϫ 10 Ϫ6 W kg Ϫ1 ) and (when between 10 Ϫ12 and 10 Ϫ6 K 2 s Ϫ1 ) can be resolved from within a factor of 2 (detailed analysis of noise level in Kocsis et al 1999). In Lake Baikal values varied actually from 8.0 ϫ 10 Ϫ12 to 4.3 ϫ 10 Ϫ7 W kg Ϫ1 for ⑀ and from 8 ϫ 10 Ϫ13 to 3 ϫ 10 Ϫ6 K 2 s Ϫ1 for .…”

Section: Rates Of Dissipation Of Tke ⑀ [W Kgmentioning

confidence: 99%

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Small‐scale turbulence and vertical mixing in Lake Baikal

Ravens

Kocsis

Wüest

et al. 2000

Limnology & Oceanography

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The water column of Lake Baikal is extremely weakly-but permanently-stratified below 250 m. Despite the thickness of this relatively stagnant water mass of more than 1000 m, the water age (time since last contact with the atmosphere) is only slightly more than a decade, indicating large-scale advective exchange. In the stratified deep water, the fate of water constituents is determined by the combined action of advective processes (deep-water intrusions) and small-scale turbulent vertical diffusion.Here, vertical diffusivity is addressed through the analysis of 25 temperature microstructure profiles collected in the three major basins of Lake Baikal to a depth of 600 m. In addition, in the 1,432-m deep south basin, monthly CTD profiles and a two year record of near-bottom currents were analyzed. Balancing turbulent kinetic energy and small-scale temperature variance leads to the conclusions that (1) vertical diffusivity in the stratified deep water ranges from 10-90 ϫ 10 Ϫ4 m 2 s Ϫ1 (between 600 and 250 m), which is three orders of magnitude more than estimated by Killworth et al. (1996), (2) the mixing efficiency is ϳ0.16, comparable to that found in stronger stratification (e.g., the ocean interior), (3) turbulence under ice decays with a time scale of 40 Ϯ 2 d and (4) the interior of the permanently stratified deep water below 250 m and the bottom boundary layer contribute roughly equally to the TKE production. The latter implies, that mixing in the deep water of Lake Baikal's three sub-basins is dominated by bottom boundary mixing as found in smaller lakes and ocean basins. Lake Baikal, located in the Great Baikal Rift zone in eastern Siberia, is by volume (23,015 km 3 ) and by depth (maximum: 1,632 m) the earth's largest freshwater body (Shimaraev et al. 1994). Since Lake Baikal is one of the oldest freshwater basins (Golubev et al. 1993) and because it faces extreme conditions, including several months of ice cover, large depth, a long water residence time (ϳ350 years), and low nutrient concentration, it developed to a unique ecosystem, which gives habitat to more than 1,500 endemic species (Martin, 1994). Topographically, the lake consists of three main basins (south, middle, and north) which are formed by sills reaching up to about 300 m (Fig. 1). The south basin (maximum depth: 1,432 m) is the main focus of this study.As with most temperate natural waters, during the summer the vertical temperature gradient of Lake Baikal is positive throughout the entire water column leading to stable density stratification with surface temperature above 14ЊC. Since the temperature of maximum density T md [ЊC] of near-surface AcknowledgmentsWe are indebted to Mike Schurter and Ruslan Gnadovsky for their help with the field campaign. We thank Michael Sturm and Rolf Kipfer for logistic and organizational support, the Swiss Federal office for Education and Science (BBW) for financial support, and Daniel Schenker for mathematical assistance in analysis of the velocity spectra. Current and thermister data were obta...

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Section: ϫ10supporting

confidence: 88%

Section: Rates Of Dissipation Of Tke ⑀ [W Kgmentioning

confidence: 99%

Small‐scale turbulence and vertical mixing in Lake Baikal

Ravens

Kocsis

Wüest

et al. 2000

Limnology & Oceanography

View full text Add to dashboard Cite

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“…In contrast, most lakes are well embedded within a terrestrial environment, with which they are strongly interacting [e.g., Kocsis et al, 1999;Schladow et al, 2002]; and the atmospheric conditions near the lake's surface are only partially determined by the exchange processes that occur over the lake itself. From the standpoint of regional and local meteorology, the fractional cover of the lakes examined in this paper is small compared to the terrestrial surface surrounding them.…”

Section: Discussionmentioning

confidence: 99%

“…The contribution of heat flux has been included in one formulation for gas fluxes Schluessel, 1994, 2001], but this was derived for the oceans and has not been satisfactorily applied to small lakes [Anderson et al, 1999]. Lakes are often topographically sheltered, affording them protection against strong winds [Schladow et al, 2002;Kocsis et al, 1999], which makes the application of oceanographically derived formulations questionable under such conditions [Schladow et al, 2002]. Cole et al [1994] showed that CO 2 flux from small lakes to the atmosphere can be a large component of the carbon budget, and even of the surrounding landscape [Kling et al, 1991[Kling et al, , 1992Richey et al, 2002].…”

Section: Introductionmentioning

confidence: 99%

CO₂ exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: Importance of convective mixing

et al. 2003

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[1] CO 2 exchange between lake water and the atmosphere was investigated at Toolik Lake (Alaska) and Soppensee (Switzerland) employing the eddy covariance (EC) method. The results obtained from three field campaigns at the two sites indicate the importance of convection in the lake in driving gas flux across the water-air interface. Measurements were performed during short (1-3 day) periods with observed diurnal changes between stratified and convective conditions in the lakes. Over Toolik Lake the EC net CO 2 efflux was 114 ± 33 mg C m À2 d À1 , which compares well with the 131 ± 2 mg C m À2 d À1 estimated by a boundary layer model (BLM) and the 153 ± 3 mg C m À2 d À1 obtained with a surface renewal model (SRM). Floating chamber measurements, however, indicated a net efflux of 365 ± 61 mg C m À2 d À1 , which is more than double the EC fluxes measured at the corresponding times (150 ± 78 mg C m À2 d À1 ). The differences between continous (EC, SRM, and BLM) and episodic (chamber) flux determination indicate that the chamber measurements might be biased depending on the chosen sampling interval. Significantly smaller fluxes ( p < 0.06) were found during stratified periods (51 ± 42 mg C m À2 d À1 ) than were found during convective periods (150 ± 45 mg C m À2 d À1 ) by the EC method, but not by the BLM. However, the congruence between average values obtained by the models and EC supports the use of both methods, but EC measurements and the SRM provide more insight into the physical-biological processes affecting gas flux. Over Soppensee, the daily net efflux from the lake was 289 ± 153 mg C m À2 d À1 during the measuring period. Flux differences were significant ( p < 0.002) between stratified periods (240 ± 82 mg C m À2 d À1 ) and periods with penetrative convection (1117 ± 236 mg C m À2 d À1 ) but insignificant if convection in the lake was weak and nonpenetrative. Our data indicate the importance of periods of heat loss and convective mixing to the process of gas exchange across the water surface, and calculations of gas transfer velocity using the surface renewal model support our observations. Future studies should employ the EC method in order to obtain essential data for process-scale investigations. Measurements should be extended to cover the full season from thaw to freeze, thereby integrating data over stratified and convective periods. Thus the statistical confidence in the seasonal budgets of CO 2 and other trace gases that are exchanged across lake surfaces could be increased considerably.

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“…The respective fluctuation spectra in the wave-number domain were fitted to the theoretical Batchelor spectrum with and (the dissipation rate of temperature variance) as the fitting parameters. The probe, the data acquisition, and the data processing procedure were described in detail in Kocsis et al (1999) and Jonas et al (2003).…”

Section: Data Processingmentioning

confidence: 99%

Breathing sediments: The control of diffusive transport across the sediment—water interface by periodic boundary‐layer turbulence

Lorke

Müller

Maerki

et al. 2003

Limnology & Oceanography

190

188

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We performed combined in situ measurements of bottom boundary-layer turbulence and of diffusive oxygen fluxes at the sediment-water interface in a medium-sized mesotrophic lake. The turbulence was driven by internal seiching with a period of 18 h. This periodic forcing, a prominent feature of enclosed water bodies, led to distinct deviations of the structure and the dynamics of the bottom boundary layer from the classical law-of-the-wall theory. A major feature was a phase lag between the current velocity and the turbulent energy dissipation of approximately 10% of the seiching period (1.5-2 h). The oxygen flux into the sediment was controlled by the diffusive boundary layer, the thickness of which varied between 0.16 and 0.84 mm during the course of a seiching period, and was strongly affected by the periodic bottom boundary-layer turbulence. The rate of dissipation of turbulent energy in the bottom boundary layer allowed us to define the Batchelor length for dissolved oxygen, which quantifies the smallest scales of oxygen fluctuations and provides an appropriate scaling for the diffusive boundary-layer thickness and the corresponding oxygen fluxes. An analysis of the governing time scales revealed the importance of turbulence in controlling the small-scale spatial heterogeneity of the diffusive fluxes. Higher turbulence causes the diffusive boundary layer (DBL) to follow the sediment topography more smoothly, resulting in an increased area-averaged flux due to the greater effective surface area.After surface zones, the bottom boundary layer (BBL) is the second prime site for animals, plants, and microorganisms in natural waters. From a physical and geochemical point of view, the importance of the BBL is twofold. First, the BBL is a major energy sink for basin-scale currents due to bottom friction and also due to the breaking of propagating internal waves on sloping bottoms (Imberger 1998). Consequently, the level of turbulence is enhanced in the BBL compared with the interior water body. Second, the BBL controls the exchange of solutes and particles between water and sediment. The sediment surface is usually an enormous sink of oxygen due to the processes caused by the decomposition of organic matter. Furthermore, the redissolution and subsequent vertical transport of ions and other solutes supply primary producers with nutrients and affect the stability of the water column by chemical (salinity) stratification (Wüest and Gloor 1998).Especially in eutrophic and mesotrophic systems with 1 Corresponding author (andreas.lorke@eawag.ch). AcknowledgmentsWe thank C. Dinkel and M. Schurter for their great help in the field. D. McGinnis kindly improved the English. We gratefully acknowledge the helpful criticism of two unknown reviewers.

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Comparison of dissipation of turbulent kinetic energy determined from shear and temperature microstructure

Cited by 84 publications

References 30 publications

Small‐scale turbulence and vertical mixing in Lake Baikal

Small‐scale turbulence and vertical mixing in Lake Baikal

CO₂ exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: Importance of convective mixing

Breathing sediments: The control of diffusive transport across the sediment—water interface by periodic boundary‐layer turbulence

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Comparison of dissipation of turbulent kinetic energy determined from shear and temperature microstructure

Cited by 84 publications

References 30 publications

Small‐scale turbulence and vertical mixing in Lake Baikal

Small‐scale turbulence and vertical mixing in Lake Baikal

CO2 exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: Importance of convective mixing

Breathing sediments: The control of diffusive transport across the sediment—water interface by periodic boundary‐layer turbulence

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Product

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CO₂ exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: Importance of convective mixing