Application of Weighted Total Acceleration Equation on Wavelength Calculation

Abstract

In this research, total acceleration equation is formulated where there is time scale coefficient at its time differential term. The formulation was done based on Courant Number equation and by using Taylor series. Then this total acceleration is applied to kinematic free surface boundary condition and Euler momentum equations. Potential velocity and water surface equations of linear water wave theory as well as wave number conservation equation were substituted to momentum and kinematic free surface boundary condition equations produced dispersion equation with wave amplitude as its variable and which fits with wave number conservation equation. Wave number conservation equation is an equation that regulates changes in wavelength as a result of water depth changes. This equation was extracted from potential velocity equation.