Physical Oceanography, Vol. 13, No. 5, 2003
FORCED OSCILLATIONS IN A BOUNDED BASIN OF VARIABLE DEPTH
N. A. Miklashevskaya
We study forced long-wave oscillations of a liquid in a ring-shaped basin of variable depth with-
in the framework of the linear theory of long waves with regard for the influence of the Coriolis
force. The oscillations are induced by disturbances of atmospheric pressure periodic as functions
of time. The parameters of the basin (bottom topography and linear sizes) are chosen to approxi-
mate the Antarctic region located between
S. The wave velocities and the structure
of the modes of elevations of the free surface are determined by using numerical methods. We
also establish the dependences of the characteristics of the wave process on the period of surface
Under the assumptions of the general linear theory of waves, free oscillations of a homogeneous inviscid li-
quid in a nonrotating ring-shaped basin of constant depth were studied in . The results of this investigation
can be found in monograph . The solution of a similar problem for a homogeneous ideal liquid filling a circu-
lar basin was obtained within the framework of the theory of long waves and the general linear theory in [2–5].
Numerical methods were used in [6–8] to study the influence of the Coriolis force and the geometric parameters
of the basin on the free oscillations of an inviscid liquid in a ring-shaped basin of variable depth. In the present
work, we study forced oscillations of the liquid in a ring-shaped basin of variable depth. As the geometric par-
ameters of the basin, we use typical characteristics of the Antarctic region [9, 10].
2. Statement of the Problem
We consider a ring-shaped basin of variable depth filled with a homogeneous inviscid liquid.
The depth of
the basin depends on a single space coordinate
It is assumed that the waves are long and oscillations are small.
The action of the Coriolis force is taken into account.
The oscillations of the liquid are generated by disturbances
of atmospheric pressure periodic of the form
r, θ, t
) = pr s t
ψθσ( ) sin( )+ , (1)
is the amplitude of disturbances of atmospheric pressure, σ is the frequency of forced oscillations, s
is the wave number (s
), and ψ()r
In polar coordinates, the equations of motion take the form 
− v = −−gp
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
20–26, September–October, 2003. Original article submitted April 19, 2002.
0928-5105/03/1305–0259 $25.00 © 2003 Plenum Publishing Corporation 259