Mathematical Model for Mangrove Protections Toward Nearshore Process

Abstract

This research developed a mathematical model to evaluate positive effects of mangroves to nearshore process. Particular purpose of the study was to conduct the analytical calculation for the steady condition of wave energy density and wave heights distributions due to the presence of mangroves. The method used was an expansion of the equations for nearshore quantities from the general condition to the one with the existence of mangroves. First, the wave energy density was calculated analytically by solving the wave energy conservation equation. The analytic solution for energy quantity is a function of position variable, involving longshore currents component and other physical constant parameters. The next step was to insert the dissipation of wave energy flux due to wave breaking into another energy balance equation involving mangroves effects. The mangroves contribution is represented by the dissipation due to the existence of the plants in the water. Other quantities included in the model are the wave group velocity and the dissipation due to bottom friction flux. Then the wave heights distribution concerning the mangroves effect was derived from the wave energy density function governed.