Cell Method for Computing Lake Circulation

The equations of fluid motion are solved using finite differences for the three-dimensional, wind-driven circulation in a homogeneous lake of arbitrary bottom topography. The method allows arbitrary choices for the wind stress, the horizontal and vertical eddy viscosities, and the distribution of vertical eddy viscosity. For the examples investigated the nonlinear terms of the equations contributed little or nothing, indicating that lake circulation is well described by linear equations. The magnitudes of the horizontal and vertical eddy viscosities have a strong effect on the current velocity but only a minor effect on the circulation patterns. The distribution of the vertical eddy viscosity appears to play a minor role in the circulation pattern. Sample calculations indicate that some combinations of horizontal eddy viscosity, vertical eddy viscosity, and distribution of vertical eddy viscosity are nearly equivalent in that these combinations produce similar response curves, similar current velocities and circulation patterns having small differences.