Physical Oceanography, Vol.
NUMERICAL SIMULATION OF VERTICAL MOTIONS IN THE BLACK SEA
FOR THE CASE OF CONSTANT DENSITY
S. G. Demyshev
The circulation of seawater of constant density under the action of stationary wind is reproduced
by using a numerical dynamic model. The computational noise appears in the field of vertical
velocities in the form of two-step waves. We carried out a series of numerical experiments with
variable vertical resolution and the coefficient of horizontal turbulent viscosity. The improve-
ment of resolution enabled us to give a correct description (both qualitative and quantitative) of
the horizontal structure of vertical motions in the bottom layer and decreased the error in the field
of vertical velocities at depths greater than
m. We conclude that it is reasonable to take into
account the dependence of the coefficient of horizontal turbulent viscosity on the vertical coordi-
The data of numerical computations available from the literature show that the existing numerical models
reproduce basic features of the Black Sea horizontal circulation. Thus, they describe the cyclonic character of
flows for the whole year, the intensification of circulation in winter, and its weakening in summer [1, 2]. The
numerical results presented in some works reproduce anticyclonic eddies observed in hydrological surveys 
and many other specific features of circulation of waters .
It is well known  that, at middle latitudes, the geostrophic balance is predominant in the equations of mo-
tion. Hence, the vertical scales of variability of currents are smaller than the horizontal scales by several orders
of magnitude. The vertical variability is largely determined by the structure of the vertical velocity w satisfying
a fine ageostrophic balance (in numerical dynamic models, w is, as a rule, a small difference of large quanti-
ties). This is actually the main cause of difficulties encountered in reproducing the vertical circulation of waters.
However, the possibility of accurate description of vertical motions regarded as a very important dynamic
characteristic is of principal significance. It is clear that the quality of reproduction of the vertical velocity de-
pends, in particular, on the vertical resolution of the model. In the present work, on the basis of the data of num-
erical experiments, we analyze the effect of vertical resolution on the structure of the vertical velocity.
Statement of the Problem
We introduce a Cartesian coordinate system x, y, z whose axes are directed to the east, north, and verti-
cally downward, respectively, and assume that seawater is incompressible and its density is constant.
As a result,
in the Boussinesq and hydrostatic approximations, we arrive at the following system of equations in Lamb’s
()ξ v =
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
58–66, January–February, 2003. Original article submitted March 29, 2001; revision submitted May 18, 2001.
0928-5105/03/1301–0053 $25.00 © 2003 Plenum Publishing Corporation 53