Development of Linear Water Wave Dispersion Equation using Critical wave Steepness Criteria

Abstract

This study begins by examining the wavelength based on criteria of critical steep steepness, both in deep water and shallow water, and it is compared to the wave length of the linear water wave dispersion equation. It was found that the wave length of the linear water wave dispersion equation is too long. The wave length adjustment of the linear water wave dispersion equation can be done by multiplying the left part of the equation with a coefficient greater than one. Furthermore, the analytic dispersion equation is formulated using weighted total acceleration, thus there is a coefficient on the left segment of the dispersion equation. The formulation is done by assuming the small amplitude wave so that the obtained dispersion equation is as same as the dispersion equation of the linear water wave theory, but using a wave length matching the criteria of critical wave steepness. Based on critical wave steepness, it is found that the wave length of the linear wave theory is too long. To shorten it, it can be done by multiplying the left segment of the dispersion equation of the linear wave with a coefficient, where the coefficient can be obtained from critical wave steepness criteria and by analytical.