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

Development of overturning circulation in sloping waterbodies due to surface cooling

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-Benard 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

Lake surface cooling drives littoral-pelagic exchange of dissolved gases

The extent of littoral influence on lake gas dynamics remains debated in the aquatic science community due to the lack of direct quantification of lateral gas transport. The prevalent assumption of diffusive horizontal transport in gas budgets fails to explain anomalies observed in pelagic gas concentrations. Here, we demonstrate through high-frequency measurements in a eutrophic lake that daily convective horizontal circulation generates littoral-pelagic advective gas fluxes one order of magnitude larger than typical horizontal fluxes used in gas budgets. These lateral fluxes are sufficient to redistribute gases at the basin-scale and generate concentration anomalies reported in other lakes. Our observations also contrast the hypothesis of pure, nocturnal littoral-to-pelagic exchange by showing that convective circulation transports gases such as oxygen and methane toward both the pelagic and littoral zones during the daytime. This study challenges the traditional pelagic-centered models of aquatic systems by showing that convective circulation represents a fundamental lateral transport mechanism to be integrated into gas budgets. Cooling-induced horizontal circulation redistributes gases daily between littoral and pelagic lake waters under calm conditions

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

Stratified horizontal convection

Surface differential heating on a stably stratified fluid body drives an overturning circulation confined to the upper fluid region - here coined stratified horizontal convection (SHC). In this manuscript, we investigate the dynamics of SHC via laboratory experiments, exploring local and global flow properties. By considering the available potential energy of the system, we derive a unique length scale of SHC and introduce the Peclet number Pe that captures both the stabilising effect of stratification and the destabilising effect of the baroclinic adjustment. We found that Pe characterises local and global flow properties, including the fluid transport of the overturning circulation, the available mechanical energy and the flow dimensionality. Our study provides insights into the fluid dynamics of stratified environments that experience horizontal convection, such as lakes, oceans and atmospheres

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

Stratified horizontal convection

Surface differential heating on a stably stratified fluid body drives an overturning circulation confined to the upper fluid region - here coined stratified horizontal convection (SHC). In this manuscript, we investigate the dynamics of SHC via laboratory experiments, exploring local and global flow properties. By considering the available potential energy of the system, we derive a unique length scale of SHC and introduce the Peclet number Pe that captures both the stabilising effect of stratification and the destabilising effect of the baroclinic adjustment. We found that Pe characterises local and global flow properties, including the fluid transport of the overturning circulation, the available mechanical energy and the flow dimensionality. Our study provides insights into the fluid dynamics of stratified environments that experience horizontal convection, such as lakes, oceans and atmospheres

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