Physical Oceanography, Vol. 15, No. 1, 2005
THERMOHYDRODYNAMICS OF THE OCEAN
HYDRODYNAMIC PRESSURE OF LIQUID IN THE PROCESS OF MOTION OF A
REGION OF CONSTANT DISTURBANCES OVER THE FLOATING ICE COVER
A. E. Bukatov and V. V. Zharkov
We study the dependence of the hydrodynamic pressure induced in a liquid as a result of motion
of a load of constant intensity over the floating ice cover on the flexural stiffness of ice and the
character of distribution of the load over the moving region. The contribution of the deflection
of ice in the vicinity of the load and the induced flexural and flexural-gravitational waves to the
formation of the field of hydrodynamic pressure near the ice–water interface is estimated.
The phase structure of three-dimensional surface waves and the amplitude characteristics of bending strains
formed in the floating ice under the action of a moving load were studied in numerous works whose survey can
be found in [1–3]. In the present work, we develop a theoretical model and apply it to the analysis of the distri-
bution of hydrodynamic pressure induced in a liquid under an ice cover by the flexural-gravitational surface
waves formed ahead of a moving load, near this load, and in the wave trace. We study the dependences of hy-
drodynamic pressure on the flexural stiffness of ice, the velocity of motion of the load, and the type of its distri-
bution in the moving region.
1. Statement of the Problem and Basic Equations
Assume that an axially symmetric load of the form
p = pfx y
( , ), x
x + vt, (1.1)
moves along a straight line with a constant velocity v over the surface of a solid ice cover floating in a basin of
constant depth H filled with an ideal incompressible liquid.
Our aim is to study the distribution of hydrodynamic pressure
formed in the liquid (near the ice–water
interface) by the induced stationary flexural-gravitational waves. The motion of liquid is regarded as potential
and the disturbances of liquid and the amplitude of bending of ice are regarded as small. Note that, in the coor-
dinate system connected with epicenter of the moving load, the hydrodynamic pressure of liquid near the ice–
water interface ζ is given by the formula
Thus, the problem is reduced to finding the velocity potential ϕ by using the Laplace equation
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–14, January-February, 2005. Original article submitted August 4,
0928-5105/05/1501–0001 © 2005 Springer Science+Business Media, Inc. 1