Physical Oceanography, Vol.
6, March, 2011 (Ukrainian Original No.
6, November–December, 2010)
THERMOHYDRODYNAMICS OF THE OCEAN
NUMERICAL ANALYSIS AND VISUALIZATION OF FINE STRUCTURES OF
THE FIELDS OF TWO-DIMENSIONAL ATTACHED INTERNAL WAVES
Yu. D. Chashechkin,
R. N. Bardakov,
and Ya. V. Zagumennyi
In the linear approximation, we compute the patterns of two-dimensional perturbations formed in a vis-
cous exponentially stratified fluid in the process of motion of a plate at an arbitrary angle to the horizon.
The exact solution of the problem obtained in quadratures and satisfying the physically meaningful
boundary conditions is numerically analyzed. The properties of the fields are computed and described in
broad ranges of all parameters of the problem, including the length and velocity of motion of the plate,
the characteristics of stratification and viscosity of the medium, and the slope of the path. In the picture
of currents, we distinguish two groups of waves and compact nonwave singularities near the edges of a
source of generation. The results of comparison with the available data of independently performed cal-
culations and experiments reveal the existing agreement between the computed and observed pictures of
Internal waves play the role of an important element of the dynamics of marine media and the atmosphere
. They transfer energy and momentum for large distances and form spots of turbulence in the case of break-
ing , which intensifies the transport of substances in the ocean and affects the safety of flights in the atmos-
phere . Their parameters are recorded both by contact  and remote methods . Numerous theoretical and
experimental works are devoted to the investigation of the attached (leeward) internal waves formed in flowing
around the obstacles .
In view of the inconsistency of equations and boundary conditions, the numerical analyses of the wave
fields are, as a rule, performed in the linear approximation and the actual body is replaced by a collection of hy-
drodynamic sources and sinks in the approximations of viscous  and ideal exponentially stratified fluids [6,
7]. It is difficult to estimate the accuracy of these calculations because the method of evaluation of the intensity
of sources is developed solely for the case of homogeneous ideal fluid. The exact solutions of the equations for
internal waves exactly satisfying the boundary conditions are of high scientific and practical interest.
In the general case, the currents flow around the obstacles with deflection and the dependence of the proper-
ties of all components of the current on its value is not monotonic. In practice, it is customary to consider the
equivalent problem of finding the field of waves formed in the process of motion of three-dimensional bodies in
immobile fluids at any angle to the horizon [5–7].
Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia.
Corresponding author; e-mail: email@example.com.
Institute of Hydromechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–15, November–December, 2010. Original article submitted March 30,
0928–5105/11/2006–0397 © 2011 Springer Science+Business Media, Inc. 397