Physical Oceanography, Vol. 14, No. 3, 2004
NUMERICAL SIMULATION OF WAVE MOTIONS IN A CHANNEL
OF CONSTANT DEPTH
V. L. Dorofeev and L. I. Sukhikh
In the present work, we study the accuracy of description of wave motions with the help of a
numerical model for a basin of simple geometry (a channel of constant depth). To specify initial
and boundary conditions and perform the comparison with the results of numerical simulations,
we use analytic solutions of the differential and finite-difference problems. We consider two
types of water: homogeneous and stratified. The procedure of numerical integration is carried
out for a period equal to several dozens of wave periods. In the case of application of the analy-
tic solution of the discrete problem, the accuracy of the numerical solution is very high for the
entire period of computations. It is shown that the proposed numerical model satisfactorily de-
scribes wave motions and can be used for the description of geophysical processes in the regions
of the World Ocean where the role played by the wave motions is significant.
The data of satellite altimetry appearing in recent years are characterized by a fairly high accuracy [1, 2]
and can be used for the assimilation of the dynamics of seas and oceans in numerical models. Thus, in [2–4], the
data of satellite altimetry are used for the simulation of circulation in the Black Sea. The fields obtained as a re-
sult enable one to study the dynamics of the Black Sea, the seasonal behavior of the Rim Current, and the synop-
tic variability of the sea. The computed hydrophysical fields are compared with the data of hydrographic obser-
vations and exhibit satisfactory quantitative agreement. As a s specific feature of the Black Sea, one can mention
the absence of tides.
In modeling hydrophysical processes in the regions neighboring with the open ocean, an important role is
played by tides. In this case, numerical models must give satisfactory description of the wave motions (and, in
particular, of tides). In , the experiments aimed at the assimilation of the data of satellite altimetry for the
Black Sea were connected with the application of an eddy-resolving model based on primitive equations of the
hydrodynamics of the ocean . In the present work, wave motions are described by using the linear version of
this model. For numerical computations, we choose a domain of simple geometry, which enables us to compare
the fields obtained by using the model with the corresponding analytic solutions. In what follows, we consider
two statements of the problem: for homogeneous and linearly stratified liquids.
We consider a basin in the form of a zonal channel of constant depth. The origin of coordinates is located
in the southwest corner of the basin. For a homogeneous liquid, the required system of equations is reduced to
the following system of linearized equations of shallow water:
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
27, May-June, 2004. Original article submitted September 12, 2002; revision submitted October 14, 2002.
140 0928-5105/04/1403–0140 © 2004 Springer Science+Business Media, Inc.