Triad resonance of flexural gravity waves in the presence of shear current with constant vorticity

Abstract

This study examines the formation of triads of flexural gravity wave in a homogeneous fluid within the context of blocking dynamics due to the presence of shear current. This study will enable us to understand the distribution of wave energy on an ice-covered sea surface. New classes of triads for flexural gravity waves are introduced depending on the direction of wave propagation with following and opposing currents. The study reveals that triad formation occurs due to the interaction of flexural gravity waves irrespective of the presence of compression and current, which has not been found in the case of free surface gravity waves. In addition, at most, three triads are formed in the case of flexural gravity waves in the presence of following and opposing currents prior to the threshold of blocking. In contrast, at least three triads are formed for any frequency within the primary and secondary blocking limits for certain values of compressive force and current speed. On the other hand, 11 triads are formed in the presence of uniform current speed as well as in the case of linear shear current with constant vorticity for a certain frequency within the blocking limit for higher values of compressive force and current speed.