Modeling the Effect of Waves on the Diurnal Temperature Stratification of a Shallow Lake

In this paper a three-dimensional circulation model has been applied to determine the spatial distribution of the temperature and mixed-layer depth (MLD) of a medium-sized shallow lake. In order to reproduce the vertical thermal structure of the lake, the impact of waves has been incorporated using several recently published schemes. These schemes approximate the additional mixing due to the orbital motion of waves, the turbulent kinetic energy produced by waves, or both. The reference solver is the Reynolds-Averaged Navier-Stokes equations with two-equation Mellor-Yamada 2.5 turbulence closure. The wave field is characterized by bulk parameters, e.g. significant wave height. The sensitivity to the choice of the wave mixing scheme is analyzed by means of an academic test case. The accuracy of the scheme is explored through data collected in Lake Balaton. The modeled temperature profiles and MLDs match measurements much better when the effect of non-breaking surface waves is included