Deflection of broken ice caused by an external load moving along a channel

Abstract

Abstract The unsteady problem of a load moving along a channel covered with broken ice is considered. Deflection of the broken ice is described by the equation of flotating liquid. The channel has a rectangular cross-section. The fluid in the channel is inviscid and incompressible. The flow caused by deflections of broken ice is potential. The external load is modeled by a smooth localized pressure distribution which moves along the centre line of the channel at a constant speed. With the help of the Fourier transform along the channel the original problem was reduced to the problem of the wave profile across the channel, which was solved by the method of separating variables. The deflections of the broken ice are studied for large times. The solution is presented in the form of sum of local deflection near the load and infinite system of waves propagating from the load with the speed of the load. Dispersion relations, phase and group speeds of these waves are found. The formation of gravity waves in a channel covered with broken ice depending on the speed of the load is studied.