Physical Oceanography, Vol.
6, March, 2011 (Ukrainian Original No.
6, November–December, 2010)
MATHEMATICAL MODELING OF THE GENERATION OF TOPOGRAPHIC
INTERNAL WAVES BY NONSTATIONARY CURRENTS
V. F. Sannikov
In the linear statement, within the framework of long-wave approximation, we develop a mathematical
model for the numerical analysis of the fields of internal waves generated by a local unevenness of the
bottom in a nonstationary spatially homogeneous flow. For the corresponding problem, we obtain the
solution suitable for numerical calculations. We study the effects connected with periodic changes in the
direction of currents and analyze the horizontal distribution of amplitudes for a single internal mode and
the dependence of this distribution on the Coriolis parameter.
The waves formed behind the obstacles under the action of incident flows are most often encountered in the
nature. Numerous works are devoted to the simulation of leeward waves generated by stationary currents (see,
e.g., the surveys in [1, 2]). The analysis of variations of the parameters of currents as functions of time (typical
of the natural phenomena) significantly complicates the solution of the corresponding hydrodynamic problems.
Therefore, the accompanying effects are studied quite poorly. A picture of the wave fields of this sort is given
by the phase portraits of the surface waves formed in the course of motion of a pressure pulse along a circular
path  and of the elastic gravitational waves generated by concentrated loads under the conditions of combined
(linear and rotational) motion [4, 5]. The general approach to the description of kinematics of the wave wake in
the case of circular motion of a source in dispersive media is proposed in .
In the present work, on the basis of a simple hydrodynamic model , we obtain a solution of the corre-
sponding problem on long waves generated by a local unevenness of the bottom in a homogeneous nonstation-
ary flow of stratified fluid suitable for numerical analysis. We study the specific features of formation of the
field of forced internal waves caused by the changes in the direction of the current. We use the linear quasistatic
approximation and the “solid-lid” boundary condition on the surface of fluid to filter out the surface waves. It is
assumed that the horizontal scale of variations of the flow is many times larger than the lengths of generated
waves. The model proposed in  is generalized by taking into account the effect of Earth’s rotation in the ap-
-plane. The analysis of specific features of the horizontal distribution of amplitudes of a single
internal mode is performed and the dependence of this distribution on the Coriolis parameter is analyzed.
Consider a layer of inviscid incompressible continuously stratified fluid of depth
H hf (x, y)
infinite in the
H + hf (x, y) < z < 0
. The unperturbed density of the fluid
depends only on a single vertical coordinate
. The role of generator of internal waves is played by a local un-
evenness of the bottom in a spatially homogeneous nonstationary field of currents
Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol, Ukraine; e-mail: email@example.com.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
16–23, November–December, 2010. Original article submitted June 1,
410 0928–5105/11/2006–0410 © 2011 Springer Science+Business Media, Inc.