Evolution of extreme nonlinear wave fields over strongly reflective plane beaches

TL;DR

This paper investigates how high reflection rates influence the formation of extreme nonlinear waves over steep beaches, combining theoretical analysis with numerical simulations to reveal stabilization effects on wave height distribution.

Contribution

It provides the first theoretical and numerical evidence that near-unity reflection rates stabilize excess kurtosis in nonlinear wave fields over steep beaches.

Findings

High reflection rates tend to stabilize wave height distribution.

Theoretical and numerical results agree on the stabilization effect.

Reflection rates near unity influence wave nonlinearity.

Abstract

The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the leading parameter controlling the reflection rates and types of breakers. Although little is known about the effect of reflection rates on the formation of extreme nonlinear waves, some debate has arisen regarding whether high reflection rates enhance the nonlinearity at the tail of the wave height distribution. In this work, we provide theoretical evidence that at very steep beaches of smooth composition, the reflection rate near unity will tend to stabilize the excess kurtosis otherwise generated by shoaling and controlled in magnitude by the bottom slope magnitude. We further verified this result through fully nonlinear numerical simulations, reaching a good agreement.