Physical Oceanography, Vol.
6, March, 2012 (Ukrainian Original No.
6, November–December, 2011)
MATHEMATICAL MODELING OF MARINE SYSTEMS
NUMERICAL ANALYSIS OF BAROTROPIC CURRENTS ON THE BLACK-SEA SHELF
ON THE BASIS OF THE HYDRODYNAMIC MODEL DEVELOPED AT THE MARINE
HYDROPHYSICAL INSTITUTE OF THE UKRAINIAN NATIONAL ACADEMY OF
S. G. Demyshev
and N. A. Evstigneeva
We describe a three-dimensional nonlinear model of the Black Sea adapted for the numerical analyses of
barotropic currents on the shelf. The specific features of finite-difference equations appearing in the
presence of liquid boundaries are discussed. The problem of simulation of currents formed under the in-
fluence of climatic winds on the northwest shelf of the Black Sea is solved as an example. We analyze
the results of three experiments in which the Dirichlet, free-flow, and mixed-type boundary conditions
are imposed for the equations of motion in the open parts of the lateral boundaries. It is shown that the
application of the Dirichlet conditions may lead to the inadequate vertical transfer near liquid bounda-
ries. For the free-flow boundary conditions, the fields of sea level and current velocities in the near-
boundary regions are characterized by the presence of significant errors. At the same time, the mixed-
type boundary conditions enable us to decrease the errors of computed fields and describe the process of
vertical transfer more accurately.
Keywords: numerical modeling, barotropic currents, high spatial resolution, northwest shelf, open liq-
The knowledge of the circulation of coastal waters in the Black Sea is required for the solution of naviga-
tion problems and for the construction of various coastal and port facilities. To compute this circulation, it is
necessary to use a hydrodynamic model taking into account the influence of river discharge and the process of
exchange through the liquid boundary and to describe the picture of currents in the shallow-water bays and
firths. In order to reproduce the actual situation, it is necessary to be able to assimilate the incoming hydrologi-
cal information in the model. It is assumed that the final goal of a series of works devoted to the adaptation of
the model developed at the Marine Hydrophysical Institute of the Ukrainian National Academy of Sciences is
the realization of a software complex aimed at the processing of the data of hydrological surveys fairly regularly
realized in the shelf zone of the Black Sea.
At present, there are several known models of the coastal zone. In , the wind currents and the currents
caused by the discharge of rivers were studied for the winter–spring season. The effects of the bottom topogra-
Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol, Ukraine.
Corresponding author; e-mail: email@example.com.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
43–58, November–December, 2011. Original article submitted August 20,
2010; revision submitted December 7, 2010.
408 0928–5105/12/2106–0408 © 2012 Springer Science+Business Media, Inc.