Flexural Gravity Wave Resonance in the Presence of Current

Abstract

In the present work, different types of resonance associated with the flexural gravity wave motion in the presence of current are discussed. Trapping is one important class of resonance and is studied in the presence of ocean current and ice compression. The existence of a resonant wave below the cutoff value is observed and analyzed in the presence of a submerged cylinder by using the multipole expansion method. It is observed that the inclusion of the ocean current enhances the search for locating the trapped waves. Trapped mode frequency increases up to the cutoff value with an increase in the current speed and, hence, ceases to exist. Therefore, the boundary value problem has a unique solution near the upper surface for higher values of the current speed. The effect of the compressive force on trapped mode behavior is also observed. It is shown numerically that trapped waves fail to exist when the group velocity is negative for specific values of the compressive force which is a very interesting result that is obtained. Significant effects of flexural rigidity, radius, and submergence depth of the cylinder on trapped waves are also observed. On the other hand, the Bragg resonance, which is used for efficient utilization of wave energy, is analyzed in the presence of current and an undulating bottom topography by using methods of perturbation and Fourier transform. The condition for Bragg resonance in the presence of current is derived in the case of a small undulating bottom topography.