Physical Oceanography, Vol.
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
S. G. Demyshev
Within the framework of the Mellor–Yamada approach, we realize a numerical scheme for the calcula-
tion of the coefficients of turbulent viscosity and diffusion in the
-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.
The correct description of the processes running in the upper mixed layer of the Black Sea is of principal
importance for the adequate reproduction of thermodynamics of the sea and, hence, for the prediction of its state.
The formation and evolution of the upper layer in the dynamic models [1, 2] were earlier described by using the
Philander–Pacanowski approximation .
In a series of numerical calculations (e.g., see ), it was shown that the application of this approximation is
reasonable in the case of smooth structures of atmospheric fields. At the same time, for the abrupt changes in
the atmospheric situation, the Philander–Pacanowski approximation gives inadequate results. First of all, this is
explained by the fact that, unlike the Mellor–Yamada parametrization, the influence of atmospheric action in
finding the coefficients of turbulence is taken into account in the Philander–Pacanowski approximation indi-
rectly, via the Richardson number . In realizations of the numerical model used for the operative prediction
of currents in the sea in the case where it is necessary to reproduce the influence of rapid changes in the atmos-
pheric conditions, this disadvantage should definitely be removed.
The Mellor–Yamada parametrization is used in the numerical model of dynamics of the ocean developed at
the Princeton University (POM) . This model is written in the
- coordinate system and applied to the solu-
tion of the problems of diagnostics and prediction of the state of marine media. Unlike the POM, in the present
work, on the basis of the Mellor–Yamada approach, we develop and realize a numerical scheme of evaluation of
the coefficients of turbulent viscosity and diffusion in the three-dimensional model used for the operative predic-
tion of currents in the Black Sea in the
-coordinate system. We consider a one-dimensional (in the space vari-
ables) version of the Mellor–Yamada parametrization in which the advective and diffusion terms in the equa-
tions for the turbulent kinetic energy and turbulence macroscale are neglected. This approximation is reasonable
as the first step of analysis because the main problems are connected with the terms used to describe the genera-
tion and dissipation of turbulent energy. We perform the analysis of finite-difference analogs of the equations
Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol, Ukraine; e-mail: email@example.com.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
29–39, May–June, 2010. Original article submitted February 3, 2009; revi-
sion submitted April 27, 2009.
184 0928–5105/10/2010–0184 © 2010 Springer Science+Business Media, Inc.