Physical Oceanography, Vol.
THERMOHYDRODYNAMICS OF THE OCEAN
INVESTIGATION OF BAROTROPIC AND BAROCLINIC SEICHES
IN BOUNDED SEA BASINS
D. V. Alekseev, O. A. Dymova, N. A. Miklashevskaya, and L. V. Cherkesov
We present a survey of works carried out at the Wave-Theory Department of the Marine Hydro-
physical Institute of the National Academy of Sciences of Ukraine for the last ten years and de-
voted to investigation of free and forced waves in bounded basins. Our attention is focused on
the results of investigation of internal waves in basins of variable depth for the case of three-layer
stratification of the liquid. The profiles of the bottom of the basin and interfaces are regarded as
parabolic. Analytic solutions are obtained and the periods of oscillations of the free surface and
interfaces for the first and second modes are determined. The dependences of the characteristics
of baroclinic waves on the geometry of the basin and parameters of stratification are analyzed.
In the last decade, in view of the deterioration of the ecological situation in the Black Sea, the attention of
the researchers to the analysis of dynamic processes running in this region (and strongly affecting the diffusion
and transport of pollutants) permanently increases. In this connection, in 1991–2002, the Wave-Theory Depart-
ment of the Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine performed a series
of fundamental investigations devoted to the analysis of barotropic and baroclinic waves in bounded sea basins
by using both analytic and numerical methods. The data of these investigations give a new knowledge of the
physical regularities relating the characteristics of wave fields to the geometry of a basin, parameters of stratifi-
cation of marine media, and atmospheric disturbances.
1. Within the framework of the linear theory of long waves, the numerical solution of the problem of free
and forced oscillations of a homogeneous incompressible liquid in a two-dimensional basin with parabolic pro-
file of the bottom and vertical walls on the boundaries is found in [1–4] under the assumption that atmospheric
pressure is periodic in time and its amplitude varies according to a linear law. The corresponding numerical re-
sults are compared with the analytic solution for a similar basin whose depth is equal to zero on the boundary. It
is shown that the frequencies of free oscillations increase in the presence of vertical walls. The regions located
near the lateral boundaries are characterized by the different behavior of the amplitude functions of the velocity
components for basins with and without walls. Moreover, the sizes of these regions increase as the walls shift to
greater depths. The amplitude functions of elevation of the free surface obtained by using numerical and analytic
methods qualitatively coincide for the entire basin. For forced waves, the deviation of the numerical solution for
the amplitude function of elevation of the free surface from the analytic solution increases both as the frequency
of driving pressure approaches the resonance value and with the depth of the basin near the walls.
The evolution of the wave process formed under the action of surface pressures periodic as functions of
time in a similar basin without vertical walls is studied with and without taking into account the Coriolis force in
[5, 6]. The basin is filled with a homogeneous liquid. At the initial time, the liquid is not disturbed and the ac-
tion of dissipative forces is taken into account. Waves formed in the analyzed case can be regarded as the super-
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
3–16, May–June, 2004. Original article submitted February 7, 2003.
0928-5105/04/1403–0127 © 2004 Springer Science+Business Media, Inc. 127