ON USING TURBULENCE ENERGY MODELS TO DEVELOP SPECTRAL VISCOSITY MODELS

This paper briefly deals with the mathematical formulation of turbulence energy models using a finite difference grid through the vertical, and the alternative formulation using a modal approach in terms of continuous functions in the vertical. In the modal model the modes are taken as eigenfunctions of a prescribed viscosity profile. Calculations show that computed tidal current profiles determined from the turbulence energy model are quite sensitive to the formulation of mixing length within the model. Profiles computed using the modal model with a fixed viscosity profile (the time-averaged viscosity profile derived from the turbulence energy model), the magnitude of which is related to the flow, are able to reproduce current profiles of both the fundamental and higher harmonics to the same level of accuracy as those determined with the turbulence energy model. By this means an "enhanced" modal model can be developed having the same characteristics as a turbulence energy model. The significantly greater computational efficiency of the modal model (a factor of five reduction in memory and 10 in computer time) coupled with the uncertainty in mixing length formulation of the turbulence energy model, suggests that modal models are valuable alternatives to, and at present show comparable accuracy with, turbulence energy models in predicting tidal current profiles.