### SECOND-ORDER PARTIAL STANDING WAVE SOLUTION FOR A SLOPING BOTTOM

Meng-Syue Li, Qingping Zou, Yang-Yih Chen, Hung-Chu Hsu

#### Abstract

This paper presents a second-order asymptotic solution in Lagrangian description for a nonlinear partial standing wave over a sloping bottom. The particle trajectories are obtained as a function of the nonlinear ordering parameters, wave steepness and the bottom slope to the second order. The analytical Lagrangian solution assumes irrotational flow and satisfies the boundary condition of constant pressure p = 0 at the free surface. This solution is applicable to progressive, standing and partial standing waves, shoaling from deep to shallow water. Mass transport and particle trajectory nonlinear partial standing waves on a sloping bottom are investigated using the closed form Lagrangian wave solution

#### Keywords

Lagrangian solution; partial standing wave; sloping bottom; mass transport, particle trajectory; nonlinear waves.

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DOI: https://doi.org/10.9753/icce.v34.waves.46