Physical Oceanography, Vol. 13, No. 6, 2003
THERMOHYDRODYNAMICS OF THE OCEAN
INTERACTION OF SURFACE WAVES IN A BASIN WITH FLOATING BROKEN ICE
A. E. Bukatov and A. A. Bukatov
The multiscale method is used to obtain asymptotic expansions up to the quantities of the third
order for the elevations of the surface of the basin and the velocity potential of motion of liquid
particles in the wave disturbances formed in the process of nonlinear interaction of periodic run-
ning waves of the first and second harmonics in a homogeneous ideal incompressible liquid of
constant finite depth covered with broken ice. The dependences of the amplitude-phase structure
of disturbances on the ice thickness, depth of the basin, and the parameters of interacting har-
monics are investigated. We estimate the error of evaluation of the characteristics of the formed
vertical displacement of the surface of the basin and nonlinear mass transfer introduced by ne-
glecting the curvature of the wave profile in the expression for the velocity potential in deducing
the kinematic and dynamic surface boundary conditions for nonlinear approximations.
The process of propagation of low-amplitude surface gravitational waves in a homogeneous liquid covered
with floating ice was studied in [1–7]. The influence of ice on nonlinear waves in a shallow basin was analyzed
in [8, 9]. For a basin of any constant depth covered with broken ice, the investigation of the evolution and non-
linear interaction of periodic wave harmonics of finite amplitude was carried out in [10, 11].
The stationary transport of liquid particles in the direction of propagation of periodic waves predicted by
the Stokes theory  was studied for a liquid with open surface in basins of infinite [13–15] and finite [16– 19]
The influence of floating broken ice on the mass transfer by periodic running surface waves of finite ampli-
tude and by the wave motion formed as a result of nonlinear interaction of progressive waves of the first and
second harmonics was studied in [10, 11, 20].
The behavior the amplitude-phase characteristics of nonlinear running periodic waves introduced by taking
into account the space and time dependences of the vertical displacements of the surface of the basin in the ex-
pression for the velocity potential on the surface of the basin (obtained in deducing kinematic and dynamic
boundary conditions for nonlinear approximations) was analyzed in .
In the present work, we perform a similar analysis of changes in the amplitude-phase structure of distur-
bances and nonlinear mass transfer introduced by taking into account the curvature of the wave profile in the
nonlinear approximations of equations for interacting periodic running waves of the first and second harmonics.
Statement of the Problem
Assume that a homogeneous ideal incompressible liquid fills an infinite basin of finite depth H and its sur-
face is covered with floating ice. We study the influence of ice on the propagation of periodic waves of low but
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol. Translated from Morskoi Gidrofizicheskii Zhurnal,
3–22, November–December, 2003. Original article submitted June 11, 2002.
0928-5105/03/1306–0313 $25.00 © 2003 Plenum Publishing Corporation 313