Turbulence modeling in ocean circulation problems

A physical formulation of the problem is considered. A mathematical model and a numerical algorithm of the turbulence model as part of the ocean circulation model for simulations for decades are formulated. The model is based on the evolution equations for turbulent kinetic energy (TKE) and the frequency of its viscous dissipation. A numerical solution algorithm for both the circulation model and the turbulence model is based on implicit schemes of splitting with respect to physical processes and geometric coordinates. For the turbulence model, this provided analytical solutions at a splitting step related to TKE generation and dissipation. Numerical experiments have been performed with a model of the joint circulation of the North Atlantic, the Arctic Ocean, and the Bering Sea to reproduce the annual cycle and synoptic disturbances of ocean characteristics. The model has a resolution of 0.25° in latitude and longitude and 40 levels in the vertical, which are compressed toward the surface to reproduce the process of developed turbulence better. The results are compared with observations and with the results of simulations using traditional parameterizations of the upper ocean mixing. It is shown that the model reproduces ocean characteristics correctly, only slightly increasing the computation time in comparison with simple parameterizations. Spatial and temporal characteristics of turbulence are analyzed.