A splitting turbulence algorithm for mixing parameterization in the ocean circulation model

Abstract

A new algorithm is proposed for solving the k-omega turbulence equations embedded in the Ocean general circulation model (OGCM). Both the circulation and turbulence models are solved using the splitting method with respect to physical processes. We split the turbulence equations into the two stages describing transport–diffusion and generation–dissipation processes. At the generation–dissipation stage, the equation for omega does not depend on turbulent kinetic energy (TKE) k. It allows us to solve both turbulence equations analytically. The technique allows us to use the same time step as in the OGCM that ensures high computational efficiency. The OGCM has a horizontal resolution of 0.25 degree and 40 sigma-levels along the vertical. The coupled model is used to simulate the hydrophysical fields of the North Atlantic and Arctic Ocean. Using the analytical solution for the k-omega turbulence model increases adequacy in reproducing oceanic characteristics by varying coefficients of this solution in numerical simulations. We present the assessments of sensitivity to variations in TKE inflow at the ocean surface. A high sensitivity of the ocean vertical structure to variations in the analytical solution coefficients is revealed at the generation–dissipation stage. In the analytical solution, we use the stability function obtained with solving the Reynolds equations. This improves reproduction of the Arctic upper desalination layer and North Atlantic and Nordic Seas upper quasi-homogeneous layer depth, comparing to using the simple form of the Prandtl number dependence on the Richardson number.