Sensitivity of the Ocean Circulation Model to the k-ω Vertical Turbulence Parametrization

Abstract

An ocean general circulation model (OGCM) of the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences with embedded k–ω vertical turbulent exchange model is developed based on the equations for turbulence kinetic energy k and energy dissipation frequency ω. The solution of the k–ω model equations depends on the frequencies of buoyancy and velocity shift simulated by the OGCM, and the coefficients of vertical turbulence depend on k and ω. The numerical algorithms of both models are based on the method of splitting by the physical processes. The k-ω model equations are split into two stages describing the three-dimensional transport-diffusion of the turbulence kinetic energy k and frequency ω and their local generation-dissipation. The system of ordinary differential equations, arising at the second stage, is solved analytically, which ensures algorithm efficiency. The analytical solution of the equation is also obtained for the vertical turbulence coefficient. The model is used to study the sensitivity of the model circulation of the North Atlantic–Arctic Ocean to variations in the parameters of vertical turbulence. The experiments show that varying the coefficients of the analytical solution of the k–ω model can improve the adequacy of the simulation. The preliminary comparison of the features of the k–ω and k–e turbulence models is presented using the method of splitting when they are employed in the OGCM.