Flexural-gravity wave dissipation under strong compression and ocean current near blocking point

Abstract

Flexural-gravity wave propagation in a dissipative sea-ice under the influence of strong compressive force and ocean current is studied. The dissipation is caused by the viscous parameter introduced in the icecovered boundary condition and results in the complex dispersion relation. The complex roots are computed using the wellestablished ML method where the initial choice is made from the roots of the dispersion relation of the non-dissipative counterpart, which poses difficulties due to the wave blocking, a phenomenon where progressive wave mode collide and wave energy propagation stops. The shift in the central wavenumber of an initial Gaussian disturbance as it propagates through the dissipative compressed ice is shown following the method proposed by Muschietti and Dum (DOI:10.1063/1.860877) when the initial central wavenumber matches and/or around the blocking wavenumber. The transformation of the location and decay of maximum amplitude and group velocity over time is shown. The effects of ice thickness and in-plane compression are also demonstrated. A small decrease in central wavenumber is shown, while the group velocity increases/decreases around the primary/secondary blocking wavenumber. Further extensive research on this method is required to incorporate the effects of other modes corresponding to the frequency of the initial central wavenumber.