Development of overturning circulation in sloping waterbodies due to surface cooling

This work was supported by the Swiss National Science Foundation (project Buoyancy driven nearshore transport in lakes, HYPOlimnetic THErmal SIphonS, HYPOTHESIS, reference 175919) and by the Physics of Aquatic Systems Laboratory (APHYS), EPFL.Cooling the surface of freshwater bodies, whose temperatures are above the temperature of maximum density, can generate differential cooling between shallow and deep regions. When surface cooling occurs over a long enough period, the thermally induced cross-shore pressure gradient may drive an overturning circulation, a phenomenon called ‘thermal siphon’. However, the conditions under which this process begins are not yet fully characterised. Here, we examine the development of thermal siphons driven by a uniform loss of heat at the air–water interface in sloping, stratified basins. For a two-dimensional framework, we derive theoretical time and velocity scales associated with the transition from Rayleigh–Bénard type convection to a horizontal overturning circulation across the shallower sloping basin. This transition is characterised by a three-way horizontal momentum balance, in which the cross-shore pressure gradient balances the inertial terms before reaching a quasi-steady regime. We performed numerical and field experiments to test and show the robustness of the analytical scaling, describe the convective regimes and quantify the cross-shore transport induced by thermal siphons. Our results are relevant for understanding the nearshore fluid dynamics induced by nighttime or seasonal surface cooling in lakes and reservoirs.Swiss National Science Foundation (SNSF) European Commission 175919Physics of Aquatic Systems Laboratory (APHYS), EPF

Seasonality modulates wind-driven mixing pathways in a large lake

Turbulent mixing controls the vertical transfer of heat, gases and nutrients in stratified water bodies, shaping their response to environmental forcing. Nevertheless, due to technical limitations, the redistribution of wind-derived energy fuelling turbulence within stratified lakes has only been mapped over short (sub-annual) timescales. Here we present a year-round observational record of energy fluxes in the large Lake Geneva. Contrary to the standing view, we show that the benthic layers are the main locus for turbulent mixing only during winter. Instead, most turbulent mixing occurs in the water-column interior during the stratified summer season, when the co-occurrence of thermal stability and lighter winds weakens near-sediment currents. Since stratified conditions are becoming more prevalent –possibly reducing turbulent fluxes in deep benthic environments–, these results contribute to the ongoing efforts to anticipate the effects of climate change on freshwater quality and ecosystem services in large lakes

Under-ice convection dynamics in a boreal lake

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, hCML (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 hCML 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

Mechanical energy budget and mixing efficiency for a radiatively heated ice-covered waterbody

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, , 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 to available potential energy, . We find that results from a competition among 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 , , where and are the change of background potential energy and the time-integrated over . The above definition is applied to estimate for the first time, finding an approximate value of . 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

Energetics of Radiatively Heated Ice-Covered Lakes

We derive the mechanical energy budget for shallow, ice-covered lakes energized by penetrative solar radiation. Radiation increases the available and background components of the potential energy at different rates. Available potential energy drives under-ice motion, including diurnally active turbulence in a near-surface convective mixing layer. Heat loss at the ice-water interface depletes background potential energy at a rate that depends on the available potential energy dynamics. Expressions for relative energy transfer rates show that the pathway for solar energy is sensitive to the convective mixing layer temperature through the nonlinear equation of state. Finally, we show that measurements of light penetration, temperature profiles resolving the diffusive boundary layer, and an estimate of the kinetic energy dissipation rate can be combined to estimate the forcing rate, the rate of heat loss to the ice, and efficiencies of the energy pathways for radiatively driven flows. Plain Language Summary Global observations reveal a pervasive decline in the annual ice cover duration of inland waters. This has stimulated urgent new research into cold and polar aquatic environments. Predicting thermal changes in ice-covered waters requires the extension of current fluid-dynamical theories to incorporate the physics that governs cold water near its temperature of maximum density. In this work, we present new mathematical expressions for the transformation of solar energy that penetrates the ice and show that feasible under-ice measurements can be used to estimate the fraction of this energy that is transferred to the ice as heat, contributing to its rate of melting

Temporal variability in thermally-driven cross-shore exchange: the role of semidiurnal tides

We examine temporal variability of thermally-driven baroclinic cross-shore exchange in the context of a tropical fringing reef system focusing on the role of tidally driven alongshore flow. Ensemble diurnal phase averaging of crossshore flow at the Kilo Nalu Observatory (KNO) in Oahu, Hawaii shows a robust diurnal signal associated with an unsteady buoyancy/diffusive dynamic balance, although significant variability is observed at sub-diurnal timescales. In particular, persistent fortnightly variability in the cross-shore diurnal flow pattern is consistent with modulation by the semidiurnal alongshore tidal flow. The alongshore flow plays a direct role in the cross-shore exchange momentum balance via Coriolis acceleration but also affects the cross-shore circulation indirectly via its influence on vertical turbulent diffusion. An idealized linear theoretical model for thermally driven cross-shore flow is formulated using the long-term time-averaged diurnal dynamic balance at KNO as a baseline. The model is driven at leading order by the surface heat flux, with contributions from the alongshore flow and cross-shore wind appearing as linear perturbations. Superposition of the idealized solutions for Coriolis and time-varying eddy viscosity perturbations are able to reproduce key aspects of the fortnightly variability. Modifying the model to consider a more realistic alongshore flow and considering effects of nightly convection lead to further improvements in comparisons with KNO observations. The ability of the theoretical approach to reproduce the fortnightly patterns indicates that semidiurnal variations in the alongshore flow are effective in modulating the cross-shore flow via Coriolis and vertical turbulent transport mechanisms

High variability in cross-shore thermally driven exchange

The variability of cross-shore thermally driven exchange was examined using ensemble averages of observations from the Kilo Nalu Observatory on the south shore of Oahu Hawaii. The cross-shore vertical shear, top-bottom temperature difference, and cross-shore advective heat flux were analyzed to evaluate the influence of the surface heat flux, the cross-shore wind and the M2 tide in the cross-shore exchange variability. The M2 affects the exchange through the effects of tidally driven alongshore flow on turbulent diffusivity and on Coriolis driven cross-shore accelerations. Lunar phase ensemble averages are compared with a theoretical model to show that the interaction of the diurnal wind pattern and the tidally driven alongshore flow can lead to significant cross-shore exchange variability at sub-diurnal time scales

Differential Heating Drives Downslope Flows that Accelerate Mixed-LayerWarming in Ice-Covered Waters

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

Horizontal transport under wind-induced resonance in stratified waterbodies

Periodic winds acting on a stratified waterbody can amplify normal modes of motion and enhance the basin-scale circulation via resonance. Here, we use idealized largeeddy simulations to investigate the flow features and quantify the horizontal transport in periodically wind-forced stratified basins. Motivated by observations in lakes, we focus on systems in which daily winds either resonate with the second vertical basin-scale internal mode, V2H1 (case 1), or the first vertical basin-scale internal mode, V1H1 (case 2). In particular, we analyze the case when strong nonlinearities affect the evolution of the V2H1 mode (case 3). To achieve these three resonance scenarios, we hold the basin morphology and the periodic forcing invariant, but change the background stratification. Our results show that a quasilinear V2H1 modal response has more active mass transport in the boundary regions than does the quasilinear V1H1 case. This difference arises from the lack of midlayer horizontal transport in the V1H1 mode, whereas the midlayer current in the V2H1 mode intensifies the transport along the slopes in both directions by splitting the flow into two branches, one running upslope and one running downslope. Nonlinear dynamics further amplify the along-slope transport in case 3, in which a second mode, an undular borelike wave, emerges from the periodic forcing. This study shows that the horizontal transport under wind-induced resonance is sensitive to the amplified mode of motion in the stratified basin and that nonlinear flow dynamics can considerably enhance mass transport in sloping regions

Seasonality modulates wind-driven mixing pathways in a large lake

Turbulent mixing controls the vertical transfer of heat, gases and nutrients in stratified water bodies, shaping their response to environmental forcing. Nevertheless, due to technical limitations, the redistribution of wind-derived energy fuelling turbulence within stratified lakes has only been mapped over short (sub-annual) timescales. Here we present a year-round observational record of energy fluxes in the large Lake Geneva. Contrary to the standing view, we show that the benthic layers are the main locus for turbulent mixing only during winter. Instead, most turbulent mixing occurs in the water-column interior during the stratified summer season, when the co-occurrence of thermal stability and lighter winds weakens near-sediment currents. Since stratified conditions are becoming more prevalent –possibly reducing turbulent fluxes in deep benthic environments–, these results contribute to the ongoing efforts to anticipate the effects of climate change on freshwater quality and ecosystem services in large lakes