  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.
