Modeling basin-scale internal waves in a stratified lake

Basin-scale internal waves provide the driving forces for vertical and hori zontal fluxes in a stratified lake below the wind-mixed layer. Thus, correc t modeling of lake mixing and transport requires accurate modeling of basin -scale internal waves: examining this capability with a hydrostatic, z-coor dinate three-dimensional (3D) numerical model at coarse grid resolutions is the focus of this paper. It is demonstrated that capturing the correct the rmocline forcing with a 3D mixed-layer model for surface dynamics results i n a good representation of low-frequency internal wave dynamics. The 3D est uary and lake computer model ELCOM is applied to modeling Lake Kinneret, Is rael, and is compared with field data under summer stratification condition s to identify and illustrate the spatial structure of the lowest-mode basin -scale Kelvin and Poincare waves that provide the largest two peaks in the internal wave energy spectra. The model solves the unsteady Reynolds-averag ed Navier-Stokes equations using a semi-implicit method similar to the mome ntum solution in the TRIM code with the addition of quadratic Euler-Lagrang e discretization, scalar (e.g., temperature) transport using a conservative flux-limited approach, and elimination of vertical diffusion terms in the governing equations. A detailed description is provided of turbulence closu re for the vertical Reynolds stress terms and vertical turbulent transport using a 3D mixed-layer model parameterized on wind and shear energy fluxes instead of the convential eddy viscosity/diffusivity assumption. This appro ach gives a good representation of the depth of the mixed-layer at coarse v ertical grid resolutions that allows the internal waves to be energized cor rectly at the basin scale.