Physical Oceanography, Vol. 14, No. 5, 2004
INVESTIGATION OF THE SPACE STRUCTURE OF THE FREE-SURFACE PROFILE
OF FORCED CIRCULAR WAVES IN A BOUNDED BASIN OF VARIABLE DEPTH
N. V. Markova, N. A. Miklashevskaya, and L. V. Cherkesov
We perform the numerical analysis of the influence of variations of the geometric characteristics
of an annular basin of variable depth on the space structure of wave motions generated by the os-
cillations of atmospheric pressure periodic as functions of time. Within the framework of the
linear theory of long waves, we determine (with regard for the action of the Coriolis force) the
ranges of periods inside which the free surface of liquid has a fixed number of nodes. The de-
pendence of these ranges on the parameters of the basin is established and the shapes of the free-
surface profiles are compared for circular and axisymmetric waves.
The results of the analysis of free linear oscillations of a homogeneous inviscid liquid placed in a nonrotat-
ing annular basin of constant depth can be found in [1, 2]. The solution of a similar problem for a round basin
was obtained (by using the theory of long waves and the general linear theory) in [2–5]. The influence of the
Coriolis force and geometric characteristics of the basin on the free oscillations of inviscid liquid in an annular
basin was studied in [6–8]. In the present work, we perform the numerical analysis of forced oscillations in an
annular basin of variable depth and analyze the influence of the period of oscillations of atmospheric pressure,
width of the ring, and depth of the basin on the shape of the free-surface profile.
Statement of the Problem
In cylindrical coordinates (
r, θ, z
, we consider a basin of variable depth filled with a homogeneous invis-
cid liquid. The basin has the form of a ring whose inner and outer radii are equal to a
The profile of the bottom depends only on the radial coordinate r. The liquid is affected by the disturbances of
atmospheric pressure periodic as functions of time. In the chosen coordinate system, these disturbances have the
r, θ, t
) = p
is the amplitude of oscillations of the atmospheric pressure, max
1, s is the wave number
), σ is the frequency of forced oscillations, and t is time.
We assume that the waves induced by oscillations (1) are long, the oscillations are regarded as small, and
the action of the Coriolis force is taken into account. Under these assumptions, the equations of motion take the
v = –
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
14–23, September–October, 2004. Original article submitted February 21, 2003.
266 0928-5105/04/1405–0266 © 2004 Springer Science+Business Media, Inc.