Theoretical Analysis of Nonlinear Flexural-Gravity Waves Interacting With Shear Currents in Polar Seas

Abstract In polar oceans, wave-current interactions are significantly affected by wind stress and bottom friction, while current velocity varies with depth due to vorticity. This study uses a perturbation method to analyze wave-current interactions beneath polar ice sheets up to the third-order approximation. The results indicate that wave steepness significantly affects the dispersion relation curve, causing the frequency to shift to higher values with increasing wave steepness for the same wavenumber. In addition, the presence of compressive forces leads to an increase in the nonlinear amplitude, indicating that the compressive forces of the ice sheet can affect the nonlinear water level variations beneath it.