Abstract. When lakes experience surface cooling, the shallow littoral region cools faster than the deep pelagic waters. The lateral density gradient resulting from this differential cooling can trigger a cold downslope density current that intrudes at the base of the mixed layer during stratified conditions. This process is known as a thermal siphon (TS). TSs flush the littoral region and increase water exchange between nearshore and pelagic zones; thus, they may potentially impact the lake ecosystem. Past observations of TSs in lakes are limited to specific cooling events. Here, we focus on the seasonality of TS-induced lateral transport and investigate how seasonally varying forcing conditions control the occurrence and intensity of TSs. This research interprets 1-year-long TS observations from Rotsee (Switzerland), a small wind-sheltered temperate lake with an elongated shallow region. We demonstrate that TSs occur for more than 50 % of the days from late summer to winter and efficiently flush the littoral region within ∼10 h. We further quantify the occurrence, intensity, and timing of TSs over seasonal timescales. The conditions for TS formation become optimal in autumn when the duration of the cooling phase is longer than the time necessary to initiate a TS. The decrease in surface cooling by 1 order of magnitude from summer to winter reduces the lateral transport by a factor of 2. We interpret this transport seasonality with scaling relationships relating the daily averaged cross-shore velocity, unit-width discharge, and flushing timescale to the surface buoyancy flux, mixed-layer depth, and lake bathymetry. The timing and duration of diurnal flushing by TSs relate to daily heating and cooling phases. The longer cooling phase in autumn increases the flushing duration and delays the time of maximal flushing relative to the summer diurnal cycle. Given their scalability, the results reported here can be used to assess the relevance of TSs in other lakes and reservoirs.
We investigated radiatively driven under-ice convection in Lake Onego (Russia) during 3 consecutive late winters. In ice-covered lakes, where the temperature of water is below the temperature of maximum density, radiatively driven heating in the upper water column induces unstable density distributions leading to gravitational convection. In this work, we quantified the key parameters to characterise the radiatively driven under-ice convection: (1) the effective buoyancy flux, B * (driver), and its vertical distribution; (2) the convective mixed-layer thickness, h CML (depth scale); and (3) the convective velocity, w * (kinematic scale). We compared analytical w * scaling estimates to in situ observations from high-resolution acoustic Doppler current profilers. The results show a robust correlation between w * and the direct observations, except during the onset and decay of the solar radiation. Our results highlight the importance of accurately defining the upper limit of h CML in highly turbid water and the need for spectrally resolving solar radiation measurements and their attenuation for accurate B * estimates. Uncertainties in the different parameters were also investigated. We finally examined the implications of under-ice convection for the growth rate of nonmotile phytoplankton and provide a simple heuristic model as a function of easily measurable parameters.
In ice-covered lakes, penetrative radiation warms fluid beneath a diffusive boundary layer, thereby increasing its density and providing energy for convection in a diurnally active, deepening mixed layer. Shallow regions are differentially heated to warmer temperatures, driving turbulent gravity currents that transport warm water downslope and into the basin interior. We examine the energetics of these processes, focusing on the rate at which penetrative radiation supplies energy that is available to drive fluid motion. Using numerical simulations that resolve convective plumes, gravity currents, and the secondary instabilities leading to entrainment, we show that advective fluxes due to differential heating contribute to the evolution of the mixed layer in waterbodies with significant shallow areas. A heat balance is used to assess the relative importance of differential heating to the one-dimensional effects of radiative heating and diffusive cooling at the ice-water interface in lakes of varying morphologies. Plain Language SummaryLake ice cover is one of the essential climate variables defined by the World Meteorological Organization. Its evolution is affected by direct meteorological forcing and by ice-penetrating radiation that heats near-surface waters and excites buoyancy-driven fluid motions. Both effects regulate water-to-ice heat transfer and thus the ice melting rate. We show how the warming of under-ice water is impacted by differential heating of the lake shallows and the resultant transport and mixing. We present a scaling analysis that quantifies how the rate of under-ice, mixed-layer warming depends on geometrical properties of the lake morphology. Accounting for differential heating and lateral transport is essential for processed-based models of ice-covered waterbodies that go beyond one-dimensional balances.
Ice-covered waterbodies are far from being quiescent systems. In this paper, we investigate ice-covered freshwater basins heated by solar radiation that penetrates across waters with temperatures below or near the temperature of maximum density. In this scenario, solar radiation sets a radiative buoyancy flux, $\unicode[STIX]{x1D6F7}_{r}$, that forces increments of temperature/density in the upper fluid volume, which can become gravitationally unstable and drive convection. The goal of this study is twofold. We first focus on formulating the mechanical energy budget, putting emphasis on the conversion of $\unicode[STIX]{x1D6F7}_{r}$ to available potential energy, $E_{a}$. We find that $E_{a}$ results from a competition among $\unicode[STIX]{x1D6F7}_{r}$ and the irreversible mixing controlled by the diapycnal and the laminar mixing rates, respectively. Secondly, and based on the above result, we introduce an integral formulation of the mixing efficiency to quantify the rate of mixing over the relevant time scale $\unicode[STIX]{x1D70F}$, $\unicode[STIX]{x1D702}_{c}\equiv \unicode[STIX]{x0394}E_{b,\unicode[STIX]{x1D70F}}/E_{r,\unicode[STIX]{x1D70F}}$, where $\unicode[STIX]{x0394}E_{b,\unicode[STIX]{x1D70F}}$ and $E_{r,\unicode[STIX]{x1D70F}}$ are the change of background potential energy and the time-integrated $\unicode[STIX]{x1D6F7}_{r}$ over $\unicode[STIX]{x1D70F}$. The above definition is applied to estimate $\unicode[STIX]{x1D702}_{c}$ for the first time, finding an approximate value of $\unicode[STIX]{x1D702}_{c}\approx 0.65$. This result suggests that radiatively heated ice-covered waterbodies might be subject to high mixing rates. Overall, the present work provides a framework to examine energetics and mixing in ice-covered waters.
Abstract. When lakes experience surface cooling, the shallow littoral region cools faster than the deep pelagic waters. The lateral density gradient resulting from this differential cooling can trigger a cold downslope density current that intrudes at the base of the mixed layer during stratified conditions. This process is known as thermal siphon (TS). TS flushes the littoral region and increases water exchange between nearshore and pelagic zones, with possible implications on the lake ecosystem. Past observations of TS in lakes are limited to specific cooling events. Here, we focus on the seasonality of the TS-induced lateral transport and investigate how the seasonally varying forcing conditions control the occurrence and intensity of TS. We base our analysis on one year of observations of TS in Rotsee (Switzerland), a small wind-sheltered temperate lake composed of an elongated shallow region. We demonstrate that TS occurs for more than 50 % of the days from late summer to winter and efficiently flushes the littoral region in ~10 hours. We further quantify the seasonal evolution of the occurrence, intensity and timing of TS. The conditions for the formation of TS are optimal in autumn, when the duration of the cooling phase is longer than the initiation timescale of TS. The decrease in surface cooling by one order of magnitude from summer to winter reduces the lateral transport by a factor of two. We interpret this transport seasonality with scaling relationships relating the daily averaged cross-shore velocity, unit-width discharge and flushing timescale to the surface buoyancy flux, mixed layer depth and lake bathymetry. The timing and duration of the diurnal flushing by TS are associated with the duration of the daily heating and cooling phases. The longer cooling phase in autumn increases the flushing duration and delays the time of maximal flushing, compared to the summer period. Our findings based on scaling arguments can be extended to other aquatic systems to assess, at a global scale, the relevance of TS in lakes and reservoirs.
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