Ice response to an underwater body moving in a frozen channel

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Strains in the ice cover of a frozen channel, which are caused by a body moving under the ice at a constant speed along the channel, are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is modeled by a thin viscoelastic plate clamped to the channel walls. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images without account for ice deflection in the leading order. The problem of a dipole moving in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of ice and the strains in the ice cover are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform along the channel, the method of normal modes across the channel, and the truncation method for resulting infinite systems of linear equations. It was revealed that the strains in the ice strongly depend on the speed of the dipole with respect to the critical speeds of the hydroelastic waves propagating along the frozen channel. The width of the channel matters even it is much larger than the characteristic length of the ice cover.