Applying Weighted Taylor Series on Time Series Water Wave Modeling

Abstract

This study develops a time series model for water waves using a weighted Taylor series approach to analyze water wave dynamics. The model incorporates the continuity equation, Euler's momentum conservation equation, and the Kinematic Free Surface Boundary Condition, all formulated through the weighted Taylor series. By integrating the modified continuity equation across the water depth, utilizing depth-averaged velocity concepts, we derive the water surface elevation equation. Similarly, applying the Euler momentum conservation principle to the water surface yields an equation for the horizontal water particle velocity, which is subsequently converted into an expression for the horizontal depth-averaged velocity. The equations for water surface elevation and horizontal water particle velocity are solved using numerical methods. The application of the numerical model results in the generation of four distinct wave profiles: sinusoidal, Stokes, cnoidal, and solitary wave profiles, classified according to Wilson's (1963) criteria. The emergence of each wave profile type is influenced by the specified input wave height.