Physical Oceanography, Vol.
THERMOHYDRODYNAMICS OF THE OCEAN
EFFECT OF THE GEOMETRIC CHARACTERISTICS OF A BASIN
ON THE SPACE STRUCTURE OF FORCED OSCILLATIONS
N. V. Markova and L. V. Cherkesov
By the method of mathematical simulation, we study the effect of changes in the width and depth
of a ring-shaped basin with parabolic profile of the bottom on the space structure of waves gen-
erated by variations of atmospheric pressure periodic as a function of time. Our investigation is
carried out under the assumptions of the linear theory of long waves with regard for the action of
the Coriolis force. The structures of the profiles of liquid surface are compared for the cases of
free and forced waves. We also establish the dependences of the period of atmospheric distur-
bances on the geometry of the basin for which the number of nodal points of the free-surface
profile in the case of forced oscillations coincides with the number of nodal points of the profile
of liquid surface in the case of free oscillations.
In , one can find the analysis of free linear oscillations of a uniform inviscid liquid in a nonrotating ring-
shaped basin of constant depth. The solution of a similar problem for a circular basin within the framework of
theory of long waves and the general linear theory was obtained in [1
4]. In [5
7], the effect of the Coriolis
force and the geometric characteristics of a ring-shaped basin on free oscillations of an ideal liquid was studied
by using numerical methods. In the present work, we continue the investigation of wave motions of the liquid in
a ring-shaped basin of variable depth caused by the variations of surface pressure.
2. Statement of the Problem
We consider a circular basin of variable depth filled with a uniform inviscid liquid. Its depth h is regarded
as a function of a single space coordinate r. It is assumed that the waves are long and oscillations are small.
The action of the Coriolis force is taken into account. As a driving force, we use disturbances of atmospheric
pressure periodic as a function of time of the form
r, θ, t
) = pr s t
ψθσ( ) sin( )+ , (1)
is the amplitude of disturbances of atmospheric pressure, s is the wave number (
s = 0, ±
σ is the frequency of forced oscillations, and ψ
) is a dimensionless function whose maximum is equal to
In polar coordinates, the equations of motion take the form 
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
14–19, September–October, 2003. Original article submitted May 27, 2002.
0928-5105/03/1305–0253 $25.00 © 2003 Plenum Publishing Corporation 253