Physical Oceanography, Vol. 15, No. 5, 2005
THERMOHYDRODYNAMICS OF THE OCEAN
DEVELOPMENT OF FORCED NONLINEAR WAVES IN A BOUNDED BASIN
N. A. Miklashevskaya and L. V. Cherkesov
The process of development of nonlinear oscillations of the free surface of a fluid caused by the
action of a periodic mass force in a bounded basin is numerically studied within the framework
of the theory of long waves. The action of dissipative forces is taken into account. The effect of
nonlinearity and geometric characteristics of the basin on the parameters of the generated wave
field is analyzed.
The investigation of the dynamics of long nonlinear waves in bounded basins is of interest in connection
with the possibility of detection of effects absent in the linear theory. Thus, free nonlinear oscillations of a fluid
(seiches) in a bounded basin are studied in [1–5]. It is shown that if the influence of nonlinearity is significant,
then, in the course of time, higher harmonics appear in the oscillations of the free-surface level. Near the coast,
the rise of the fluid occurs faster than its lowering [1–5] and the average free-surface level no longer coincides
with the nondisturbed position . Friction smooths out these effects, since higher harmonics decay faster. In
, the analytic solution of the problem of forced waves caused by the action of a tide-forming force in channels
of constant depth was obtained in the linear statement without taking into account dissipation.
In the present work, forced nonlinear oscillations of a fluid induced in a bounded basin by a periodic mass
force are studied with regard for the action of dissipative forces.
1. Assume that a fluid fills a basin whose depth depends on a spatial coordinate x (the bottom topography
is regarded as constant along the
y-axis). Under the assumption that the fluid is homogeneous and incompressi-
ble, we get the following nonlinear system of equations of shallow water taking into account the action of dissi-
pative forces :
u g uu u
+++ζμ = X, (1)
On the vertical side walls of the basin x = 0 and x = l, we impose the following conditions of imperme-
) = 0 and u
) = 0. (3)
At the initial time (t = 0), the fluid is in the state of rest, i.e.,
) = 0 and ζ
) = 0. (4)
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–12, September–October, 2005. Original article submitted April 30,
0928-5105/05/1505–0265 © 2005 Springer Science+Business Media, Inc. 265