Problem of a Moving Load in a Channel Covered with Broken Ice
Abstract
In this paper, the effect of broken ice on the formation of gravitational waves caused by an external load moving along a channel is studied. The external load is modeled by a smooth locally distributed pressure moving along the center line of the channel at a constant speed. The governing equations are the differential equation of oscillations of thin broken ice and the Laplace equation for a flow velocity potential under the broken ice. These equations are closed by the impermeability conditions on the walls and bottom of the channel, and by the kinematic and dynamic conditions at the broken ice-liquid interface. The traveling wave solution that does not depend on time in a coordinate system moving together with the external load is investigated. Using the Fourier transform along the channel the problem under consideration reduces to a two-dimensional problem with respect to the profile of the gravitational wave across the channel, which is solved by the method of separation of variables. The analysis of the formation of gravitational waves in the broken ice is provided. It is shown that for every speed of the load there is a countable number of gravitational waves propagating along the channel with the velocity of the load. Each wave has a given profile across the channel. An example of test calculations for a three-dimensional problem is shown.
DOI 10.14258/izvasu(2018)4-13
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