Stochastic particle transport by deep-water irregular breaking waves

TL;DR

This paper develops a stochastic model combining Brownian motion and a compound Poisson process to predict particle transport by irregular deep-water waves, validated through experiments showing enhanced transport with wave breaking.

Contribution

It introduces a novel stochastic differential equation model that accounts for both non-breaking and breaking wave effects on particle transport, including jumps and skewness.

Findings

Particle position variance grows linearly with time.

Breaking waves increase transport variability and skewness.

Model predictions align with experimental observations.

Abstract

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by deep-water breaking waves is enhanced compared to non-breaking waves. To model particle transport in irregular waves, some of which break, we develop a stochastic differential equation describing both mean particle transport and its uncertainty. The equation combines a Brownian motion, which captures non-breaking drift-diffusion effects, and a compound Poisson process, which captures jumps in particle positions due to breaking.We corroborate these predictions with new experiments, in which we track large numbers of particles in irregular breaking waves. For breaking and non-breaking wave fields, our experiments confirm that the variance of the particle position grows linearly with time, in accordance with Taylor's single-particle dispersion theory. For wave fields that include breaking, the compound Poisson process increases the linear growth rate of the mean and variance and introduces a finite skewness of the particle position distribution.