A three-dimensional vertical mixing model applied to Lake Kinneret

The two-dimensional, two-layer Eulerian shallow water equations have been coupled with a Lagrangian one-dimensional vertical mixed-layer turbulence closure scheme. Integrated with the advection-diffusion equation for heat, a new approach to a three-dimensional vertical mixing model is presented for Lake Kinneret. Previous Eulerian-Lagrangian models (SCHOPF & CANE 1983) explicitly incorporated the Lagrangian terms, typically the upwelling/downwelling velocities, into the hydrodynamic Eulerian flow equations. In the present approach the equations are implicitly coupled, while still forming a closed system. Subsequently only the two-dimensional two-layer hydrodynamic equations are solved on a grid covering the entire lake. The thermal structure on the other hand is not restricted by the two-layer momentum equations, but is independently defined by a system of layers according to the level of turbulence in the water column. Furthermore, the thermal structure can be solved for chosen transects, greatly alleviating the computational expenditure for solving large lake systems. The model computes the vertical thermal structure across the lake, and hence the depth of, and temperature and density jump across the thermocline, key variables in any water quality control model.