Nonlinear shallow ocean wave soliton interactions on flat beaches

TL;DR

This paper demonstrates that nonlinear shallow ocean wave interactions, resembling soliton solutions, occur daily on flat beaches and are more common than previously thought, with implications for understanding tsunami wave merging.

Contribution

It reveals the frequent occurrence of nonlinear wave interactions on beaches and links these phenomena to soliton solutions of nonlinear wave equations, challenging prior assumptions of rarity.

Findings

Nonlinear interactions occur daily near low tide on beaches.

Interactions resemble soliton solutions of nonlinear wave equations.

Implications for tsunami wave merging and coastal wave dynamics.

Abstract

Ocean waves are complex and often turbulent. While most ocean wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2,000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multi-dimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.