Oblique wave trapping in a two-layer fluid: Effect of wave blocking

Abstract

The combined effect of ocean current and ice compression on wave trapping and blocking is investigated here under the oblique incidence wave in a two-layer fluid. Both layers are assumed to be of finite depth. A submerged horizontal cylinder is placed near the interface in the lower layer to generate the trapped modes and study their properties influenced by wave blocking. The problem is formulated by using linearized water wave theory with small amplitude structural response and the multipole expansion method. Multiple branches of the dispersion relation segregate the frequency spectra into parts within which the number of propagating modes varies due to the occurrence of wave blocking, leading to multiple types of trapped modes. The effect of both the co-current and opposing current on the occurrence of the propagating modes in the positive frequency zone has been studied in detail. The behavior of such trapped modes within/outside the blocking range depends on three important parameters: current, density ratio, and ice compression. It is observed that there exists a specific range of density ratio (s) in which trapped mode occurs. Depending on the ice compression, these trapped frequencies follow the monotonicity with an increase in the density ratio.