Internal Waves under Ice Cover

Abstract

A theoretical model for propagation of internal waves under an ice cover is developed. The sea water is considered to be inviscid, non-rotating, and incompressible and the Brunt–Väisälä frequency is supposed to be constant. The ice is considered of uniform thickness, with constant values of Young's modulus, Poisson's ratio, density and compressive stress in the ice. The boundary conditions are such that the normal velocity at the bottom is zero and, at the undersurface of the ice, the linearized kinematical and dynamic boundary conditions are satisfied. We present and analyze explicit solutions for the internal waves under the ice cover and the dispersion equations. It is shown that when the frequency is near, but smaller than the Brunt–Väisälä frequency the ice deflections can be considerable. The theoretical results are compared with experimental data for the Arctic regions.