Flushing the Lake Littoral Region: The Interaction of Differential Cooling and Mild Winds

The interaction of a uniform cooling rate at the lake surface with sloping bathymetry efficiently drives cross‐shore water exchanges between the shallow littoral and deep interior regions. The faster cooling rate of the shallows results in the formation of density‐driven currents, known as thermal siphons, that flow downslope until they intrude horizontally at the base of the surface mixed layer. Existing parameterizations of the resulting buoyancy‐driven cross‐shore transport assume calm wind conditions, which are rarely observed in lakes and thereby restrict their applicability. Here, we examine how moderate winds (≲5 m s−1) affect this convective cross‐shore transport. We derive simple analytical solutions that we further test against realistic three‐dimensional numerical hydrodynamic simulations of an enclosed stratified basin subject to uniform and steady surface cooling rate and cross‐shore winds. We show cross‐shore winds modify the convective circulation, stopping or even reversing it in the upwind littoral region and enhancing the cross‐shore exchange in the downwind region. The analytical parameterization satisfactorily predicted the magnitude of the simulated offshore unit‐width discharges in the upwind and downwind littoral regions. Our scaling expands the previous formulation to a regime where both wind and buoyancy forces drive cross‐shore discharges of similar magnitude. This range is defined by the non‐dimensional Monin‐Obukhov length scale, χMO: 0.1 ≲ χMO ≲ 0.5. The information needed to evaluate the scaling formula can be readily obtained from a traditional set of in situ observations. Plain Language Summary The flushing of the littoral region is a fundamental question for local lake managers. From a physical viewpoint, exchanges between littoral and pelagic regions are largely dominated by horizontal currents. Existing parameterizations of the cross‐shore transport commonly reduce the problem to a single forcing mechanism. Wind‐driven circulation is generally the main factor explaining the flushing of shallow waters in lakes. Yet, another forcing such as differential cooling resulting from a uniform surface cooling exerted on waterbodies of varying bathymetry also drives cross‐shore transport. Briefly, shallow littoral waters become denser and generate a cross‐shore circulation cell, with denser littoral water flowing offshore near the lake bed and lighter interior water moving onshore near the surface. However, this “thermal siphon” of