Effects of Rayleigh number on thermal siphons in Triangular Water Bodies

Natural convection, driven by surface cooling, in water bodies (lake, reservoirs etc.) has been investigated in the past with emphasis on the development of thermal siphons (large-scale overturning circulation). The latter is the result of faster cooling of the shallow nearshore regions and the development of horizontal exchange between shallow and deep waters. Initially, the water body is characterized by local, quasi-isotropic convective cells, and, afterwards, a two-layer exchange flow, which characterizes the large-scale circulation, develops. Finally, a quasi-steady state is achieved during which the produced water discharge remains constant.

The numerical models used for simulating thermal siphons in water bodies, especially for high Rayleigh numbers (turbulent natural convection), are limited and belong to two categories: (a) Large Eddy Simulation (LES) models (two- or three-dimensional), which usually require significant computer resources, and (b) Reynolds-Averaged Navier Stokes (RANS) models in conjunction with a turbulence model accounting for turbulence effects.

In this study a Large Eddy Simulation (LES) approach is used for investigating thermal siphons, due to surface cooling, in water bodies for high Ra numbers. The Wall-Adapting Local Eddy Viscosity (WALE) model is selected to compute subgrid-scale turbulence effects, offering improved accuracy over classical models for domains with laminar zones. In addition, a Navier–Stokes approach, considered as “Two-Dimensional Direct Numerical Simulation”, has provided results for comparison purposes from a previous study. Temperature and stream-function fields, based on both approaches, are presented and show features of the developed thermal siphons and the interaction between downslope gravity currents and downflowing convective plumes. Comparison of the results from the two approaches indicates important differences in the development of thermal siphons and the interaction between bottom gravity currents and convective plumes.