A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling

TL;DR

This paper develops a nonlinear formulation of radiation stress and energy flux tailored for cnoidal wave shoaling, providing a new set of equations and a numerical method validated against experimental data.

Contribution

It introduces a nonlinear shoaling model based on KdV scaling and a numerical algorithm for solving the associated equations, advancing wave modeling accuracy.

Findings

The formulation accurately predicts wave transformation during shoaling.

Numerical solutions agree well with experimental data.

The model improves understanding of cnoidal wave behavior near beaches.

Abstract

In this article we provide formulations of energy flux and radiation stress consistent with the scaling regime of the Korteweg-de Vries (KdV) equation. These quantities can be used to describe the shoaling of cnoidal waves approaching a gently sloping beach. The transformation of these waves along the slope can be described using the shoaling equations, a set of three nonlinear equations in three unknowns: the wave height H, the set-down and the elliptic parameter m. We define a numerical algorithm for the efficient solution of the shoaling equations, and we verify our shoaling formulation by comparing with experimental data from two sets of experiments as well as shoaling curves obtained in previous works.