Effects of Spatial Wind Inhomogeneity and Turbulence Anisotropy on Circulation in an Elongated Basin: A Simplified Analytical Solution

The response of a closed basin to wind forcing has been studied extensively, but the role of turbulence anisotropy coupled with spatial wind inhomogeneity has never been considered explicitly. An analytical solution is presented for steady state hydrodynamics, considering the central part of a constant-depth, elongated basin with a laterally varying wind, and a homogeneous, yet anisotropic, eddy viscosity tensor. The solution is derived both for a single-layer and for a two-layer basin, which is representative of a stratified lake with a well-developed thermocline. Since the focus is on the short-term barotropic reaction to wind forcing, which determines the type of lake circulation, baroclinic effects are neglected as a first approximation. In this case, the development of planimetric (depth-averaged) circulation superimposed on circulation in the vertical plane can be determined as a function of wind lateral variation and a few dimensionless parameters. The relevance of such an analytical solution is twofold. Firstly, the knowledge of the prevailing circulation can help in the choice of the best type of numerical model (three-dimensional vs. two-dimensional, depth- or lateral-averaged). Secondly, it shows the importance of correct estimates of both vertical and horizontal eddy viscosity, whereas the latter is not usually considered as an important parameter in lake hydrodynamics modeling.