Dispersion Relation of a Two-Layer Model for Submerged Porous Breakwater
Nadhira Karima, Indriana Marcela, Ikha Magdalena

Bandung Institute of Technology

Abstract

Many fluid-dynamics models use a dispersion relation to study the waves^ characteristics throughout the observation domain. In this study, we use a dispersion relation to analyze the wave transformation in a multi-layer fluid domain containing a submerged porous breakwater. The mathematical model for this boundary value problem is derived from potential theory. Further, we use the separation of variables method to find the solution analytically. As a result, an equation representing the dispersion relation is obtained. We also conduct several simulations to study the significance of each parameter involved in the model to the reduction magnitude. From the observation, we conclude that the incoming waves^ angular frequency, porous domain length, porosity, and friction coefficient play a crucial role in decreasing the wave amplitude.

Keywords: dispersion relation, potential theory, submerged porous breakwater

Topic: Mathematics