Investigation of the sensitivity of the Mellor–Yamada parametrization to the choice of finite-difference analogs in a numerical three-dimensional model of the operative prediction of currents in the black sea

Within the framework of the Mellor–Yamada approach, we realize a numerical scheme for the calculation of the coefficients of turbulent viscosity and diffusion in the z -system of coordinates for the three-dimensional model of operative prediction of currents in the Black Sea. Some discrete analogs of the equations for turbulent kinetic energy and turbulence macroscale are studied. Their high sensitivity to the choice of finite-difference approximations is demonstrated. On the basis of the comparison of the results of prognostic experiments with the data of observations, we choose the best approximation of the term used to describe the generation pf turbulence energy.