Transport by an intrusion generated by boundary mixing in a lake

Wain, Danielle; Rehmann, Chris R.

doi:10.1029/2009wr008391

Cited by 26 publications

(21 citation statements)

References 65 publications

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“…Note, however, that the exchange of fluid between BBL and interior is not taken into account in our simple one-dimensional modeling approach. This clearly conflicts with the frequently reported evidence for intrusions, advecting mixed BBL fluid toward the interior near sloping topography (Armi 1978(Armi , 1979aPhillips et al 1986;Wain and Rehmann 2010). This additional mechanism for boundary layer restratification is likely to lead to more efficient mixing in the BBL (Wain and Rehmann 2010;Gloor et al 2000;Armi 1979b), and we expect that (42) only provides a lower bound for the basin-scale diffusivity.…”

Section: Discussioncontrasting

confidence: 72%

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

Umlauf

Burchard

2011

Journal of Physical Oceanography

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The interaction of shear, stratification, and turbulence in boundary layers on sloping topography is investigated with the help of an idealized theoretical model, assuming uniform bottom slope and homogeneity in the upslope direction. It is shown theoretically that the irreversible vertical buoyancy flux generated in the boundary layer is directly proportional to the molecular destruction rate of small-scale buoyancy variance, which can be inferred, for example, from microstructure observations. Dimensional analysis of the equations shows that, for harmonic boundary layer forcing and no rotation, the problem is governed by three nondimensional parameters (slope angle, roughness number, and ratio of forcing and buoyancy frequencies). Solution of the equations with a second-moment closure model for the turbulent fluxes reveals the periodic generation of gravitationally unstable boundary layers during upslope flow, consistent with available observations. Investigation of the nondimensional parameter space with the help of this model illustrates a systematic increase of the bulk mixing efficiencies for (i) steep slopes and (ii) low-frequency forcing. Except for very steep slopes, mixing efficiencies are substantially smaller than the classical value of G 5 0.2.

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Section: Discussioncontrasting

confidence: 72%

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

Umlauf

Burchard

2011

Journal of Physical Oceanography

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“…Predicted mixing efficiencies are much lower than the threshold of 20%, assumed for interior turbulence [ Osborn , 1980], but are substantially larger than those reported by Umlauf and Burchard [2011] in their idealized, one‐dimensional investigation of shear‐induced BBL convection. This discrepancy may be explained by our observation that the BBL on the slope exhibited a rather strong and variable stratification which, similar to the observations by Gloor et al [2000], points at an exchange between the BBL and the interior by intrusions [ Wain and Rehmann , 2010]. This effect, obviously missing in the one‐dimensional setup studied by Umlauf and Burchard [2011], provides an effective mechanism of BBL restratification with a positive feedback on the mixing efficiency.…”

Section: Resultssupporting

confidence: 54%

Boundary mixing in lakes: 2. Combined effects of shear- and convectively induced turbulence on basin-scale mixing

et al. 2011

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[1] A detailed comparison of results from a numerical three-dimensional hydrostatic lake model with high-resolution observations of the vertical structure of the turbulent bottom boundary layer (BBL) in a medium-size lake (Lake Alpnach, Switzerland) is provided. The focus of this study is on the shear-induced generation and destruction of stratification in the BBL that may ultimately lead to unstable layers (convection). The model was shown to provide a reliable description of the internal seiching dynamics, as well as the local BBL properties, including the generation of shear-induced convection in two data sets from 2003 and 2007. Basin-scale mixing parameters, inferred from the simulations, are closely connected to the seiching motions, with the hypolimnetic mixing reacting almost immediately to the variable wind-forcing and seiching activity. During upslope flow, the BBL becomes convectively turbulent, causing low mixing efficiency on a basin-scale, whereas during downslope flow, the BBL is restratifying and shear-induced turbulence is weak but leads to a higher mixing efficiency. The overall deep-water mixing efficiency varied in the range of 5 to 10% in this system dominated by turbulent boundary processes.

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“…This situation may be comparable to the onset of mixing after a longer quiescent period with low wind speeds during which BBLs have fully restratified [see Part 2]. During later times (Figure 10), BBLs in the flat central part of the basin have entrained to their maximum thickness (limiting further mixing), whereas the boundary layers on the slopes are governed by a balance between local mixing and exchange of BBL and interior fluid via intrusions [ Gloor et al , 2000; Lorke et al , 2008; Wain and Rehmann , 2010].…”

Section: Basin‐scale Effect Of Boundary Layer Mixingmentioning

confidence: 99%

Boundary mixing in lakes: 1. Modeling the effect of shear-induced convection

Becherer

Umlauf

2011

J. Geophys. Res.

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[1] Recent studies in lakes have shown evidence for a strong influence of shear-induced stratification on mixing in turbulent bottom boundary layers (BBLs) on sloping topography. These observations suggest that the periodic near-bottom shear resulting from internal wave motions may lead to alternating periods of gravitationally stable and unstable stratification in the BBL with relevant implications for turbulence and mixing in the entire basin. The impact of these processes for basin-scale mixing is investigated here in a three-dimensional processes-oriented modeling study, using a well-investigated system (Lake Alpnach, Switzerland) as an example. Consistent with available observations, our results indicate that the BBL becomes gravitationally unstable in areas with upslope flow, covering a substantial fraction of the total bottom area of the lake. While near-bottom convection associated with the unstable stratification in these areas results in strong turbulence, its contribution to net mixing is negligible since the BBL is already well mixed. Conversely, in areas with downslope flow the near-bottom shear generates stable stratification, leading to a suppression of turbulence but also to larger mixing rates due to an enhanced mixing efficiency. Overall, BBL mixing is found to dominate basin-scale mixing. These mechanisms are likely to be important for a large class of stratified natural waters, in which boundary layer mixing is energized by periodic internal waves or basin-scale motions.

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Transport by an intrusion generated by boundary mixing in a lake

Cited by 26 publications

References 65 publications

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

Diapycnal Transport and Mixing Efficiency in Stratified Boundary Layers near Sloping Topography

Boundary mixing in lakes: 2. Combined effects of shear- and convectively induced turbulence on basin-scale mixing

Boundary mixing in lakes: 1. Modeling the effect of shear-induced convection

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