# Surface waves enhance particle dispersion

## TL;DR

This study reveals that surface gravity waves cause super-diffusive particle dispersion, with variance growing quadratically over time, significantly faster than traditional linear models predict, due to long-term velocity correlations.

## Contribution

The paper demonstrates that surface waves induce super-diffusive dispersion of particles, contrasting with classical models, through exact nonlinear trajectory calculations.

## Key findings

- Particle variance grows as t^2 at large times.
- Surface waves significantly enhance particle dispersion.
- Long-term velocity correlations cause super-diffusive behavior.

## Abstract

We study the horizontal dispersion of passive tracer particles on the free surface of gravity waves in deep water. For random linear waves with the JONSWAP spectrum, the Lagrangian particle trajectories are computed using an exact nonlinear model known as the John--Sclavounos equation. We show that the single-particle dispersion exhibits an unusual super-diffusive behavior. In particular, for large times $t$, the variance of the tracer $\langle |X(t)|^2\rangle$ increases as a quadratic function of time, i.e., $\langle |X(t)|^2\rangle\sim t^2$. This dispersion is markedly faster than Taylor's single-particle dispersion theory which predicts that the variance of passive tracers grows linearly with time for large $t$. Our results imply that the wave motion significantly enhances the dispersion of fluid particles. We show that this super-diffusive behavior is a result of the long-term correlation of the Lagrangian velocities of fluid parcels on the free surface.