Physical Oceanography, Vol. 15, No. 2, 2005
INFLUENCE OF THE SPACE DISTRIBUTION OF ATMOSPHERIC
PRESSURE ON THE STRUCTURE OF FREE WAVE SURFACE IN
A BASIN OF VARIABLE DEPTH
N. V. Markova and L. V. Cherkesov
Within the framework of the linear theory of long waves, we study forced oscillation of liquid in
a ring basin of variable depth by using numerical methods. As a generator of waves, we use pe-
riodic (in time) variations of atmospheric pressure. The action of the Coriolis force is taken into
account. The liquid is regarded as homogeneous and inviscid. We analyze the dependences of
the structure of the free wave surface (the number and location of nodal lines) on the period and
space distribution of disturbing pressures.
In , free linear oscillations of a homogeneous inviscid liquid in ring basins of constant depth are studied
without taking into account the Coriolis force. The influence of Earth’s rotation and the geometric characteris-
tics of a basin on the free oscillations of an inviscid liquid in this basin are analyzed in [2–4]. For ring basins of
variable depth, the solution of the problem of forced waves induced by the action of surface pressures with linear
profile is obtained and studied in detail in [5, 6]. In the present work, we continue our investigations of forced
oscillations of a liquid generated by periodic (in time) variations of atmospheric pressure. For ring basins of var-
iable depth, we compare the profiles of the free surface of axially symmetric waves induced by the action of sur-
face perturbations with different space distributions. The influence of the period and profile of disturbing
pressures on the structure of the free surface is analyzed.
2. Statement of the Problem
We consider a basin of variable depth filled with a homogeneous inviscid liquid in a cylindrical coordinate
r, θ, z
. The basin has the form of a ring with inner and outer radii
r = a
r = a
The profile of the bottom depends only on the coordinate r. The liquid is subjected to the action of periodic (in
time) perturbations of atmospheric pressure described, in the chosen coordinate system, by the formula
r, θ, t
) = pr t
ψσ( ) sin , (1)
is the amplitude of perturbations of atmospheric pressure,
is the frequency of
forced oscillations, and t is time.
We assume that the waves generated by the perturbations of pressure (1) are long and the oscillations are
small and take into account the action of the Coriolis force. Under these assumptions, the equations of motion
take the form 
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
11–23, March–April, 2005. Original article submitted December 8,
0928-5105/05/1502–0079 © 2005 Plenum Publishing Corporation 79