Analytical Investigation of Wave Interaction with a Submerged Trench under Uniform Currents Using Evanescent Mode Theory

Ocean surface waves are strongly affected by various physical processes, leading to the formation of gravity waves propagating from offshore toward coastal areas. The interaction between these waves and submerged structures presents critical challenges in ocean engineering. This study presents an analytical investigation of surface wave interaction with a single submerged rectangular trench in the presence of a uniform current, which may be co-directional or counter-directional with respect to the direction of wave propagation.

The wave dynamics are analyzed within the framework of linear potential flow theory, assuming an incompressible, inviscid, and irrotational fluid. The analytical model is based on the evanescent mode expansion technique, which allows the representation of the velocity potential as a series of propagating and decaying modes. Boundary conditions are rigorously applied at the free surface, trench interfaces, and channel bottom. The method ensures continuity of potential and velocity across trench boundaries, accounting for the influence of current on dispersion relations.

The results show that the presence and direction of the current significantly modify the wave reflection characteristics. The trench geometry, including depth and width, also has a substantial impact on the reflection and transmission behavior. The study confirms the ability of evanescent mode theory to capture complex interactions in wave–structure systems more accurately than simpler approximations.

This work enhances the understanding of wave attenuation mechanisms due to submerged structures and supports the development of efficient analytical models for coastal protection. The findings provide guidance for future experimental validation and practical applications in marine and coastal engineering.