Unsteady bending-gravity waves in the sea with ice cover caused by moving disturbances of variable intensity
UDC
539.3:532.5DOI:
https://doi.org/10.31429/vestnik-20-1-41-51Abstract
In winter, most of the rivers and lakes of the northern regions of Russia are covered with ice. This makes navigation difficult. To prolong navigation, hovercrafts are used, which, moving at a certain speed, destroy the ice cover. On the other hand, the ice cover of rivers and lakes is used to organize crossings and delivery of various cargoes along them. Therefore, it is important to know the values of the critical velocities at which the destruction of the floating ice sheet occurs.
The paper investigates the development of three-dimensional bending-gravity waves generated by a moving source of variable intensity. The ice cover is modeled by a thin elastic isotropic plate floating on the surface of an ideal incompressible fluid of finite depth. Methods of integral Fourier and Laplace transformations are used to solve the problem. The resulting integral representation for the elevation of the plate-liquid surface is investigated by the stationary phase method for multidimensional integrals.
The values of critical velocities at which the nature of the wave disturbance changes both in front of the source of disturbances and behind it, are determined. The dependence of critical velocities on the oscillation frequency of the source is investigated. It is shown that there will be six such values of critical velocities. In the absence of source oscillations, there are three values of critical velocities.
Phase portraits of the generated waves for different ranges of the source velocity and frequency of its oscillations, as well as the fronts of the generated waves are given. It is shown that depending on the velocity of the source and the frequency of its oscillations, from one to seven wave systems are formed. The angular zones in which these waves are formed are determined.
Keywords:
bending-gravitational waves, elastic plate, ice cover, critical speedAcknowledgement
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