Oblique Water Wave Scattering by a Trench in a Two-Layer Fluid

Abstract

The problem of oblique water wave scattering and trapping by a submarine trench in a two-layer fluid is analyzed within the context of the linearized water wave theory. Under the potential flow approach, the solution of the associated boundary value problem is derived by the matched eigenfunction expansion method. Numerical results for the reflection and transmission coefficients in surface and internal waves for several physical parameters are obtained. The reflection and transmission coefficients are computed and analyzed in various configurations. The depth and width of the trench affect the reflection and transmission coefficients in both modes. For a symmetric trench, the periodicity of zero and the minimum reflection values increase as the width of the trench increases. The angle of incidence significantly affects the reflection and transmission coefficients at surface mode. In addition to the structural properties of the submarine trench, wave reflection and transmission in surface and internal modes are strongly dependent on the fluid density ratio and the interface location. The numerical results are compared with cases in the specialized literature and very good agreement is achieved. In order to verify the computational results, energy relations are derived and the numerical results are found to satisfy these relations accurately.