Dipole Oscillations along Principal Coordinates in a Frozen Channel in the Context of Symmetric Linear Thickness of Porous Ice

Abstract

The problem of periodic oscillations of a dipole, specifically its strength, along the principal axes in a three-dimensional frozen channel is considered. The key points of the problem are taking into account the linear thickness of ice across the channel and ice porosity within Darcy’s law. The fluid in the channel is inviscid and incompressible; the flow is potential. It is expected that the oscillations of a small radius dipole well approximate the oscillations of a small radius sphere at a sufficient depth of immersion of the dipole. It was found that during oscillations along the channel and vertical oscillations, waves are generated in the channel, propagating along the channel with a frequency equal to the frequency of dipole oscillations. These waves decay far from the dipole, and the rate of decay depends on the porosity coefficient.