New Weighted Taylor Series for Water Wave Energy Loss and Littoral Current Analysis

Abstract

This paper presents a more systematic formulation of the weighted Taylor series, resulting in a more accurate determination of the weighting coefficient. The weighted Taylor series is derived by truncating the Taylor series to the first order and assigning weighting coefficients to the first-order terms, which reflect the contribution of higher-order terms. The resulting weighted Taylor series is applied to the analysis of wave constant equations in deep water, including wavelength and wave period, which are primarily governed by the Kinematic Free Surface Boundary Condition. The input for these wave constant equations is the wave amplitude. Using these wave constant equations, a shoaling-breaking model is developed, accounting for wave energy loss. The lost wave energy is then utilized to derive the radiation current equation, which subsequently leads to the formulation of the littoral current equation.