A Nonlinear Formulation of Radiation Stress and Applications to Cnoidal Shoaling

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 $${\\bar{\\eta }}$$\n \n \n η\n \n \n ¯\n \n \n 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.