Breaking wave field statistics with a multilayer model

TL;DR

This paper introduces a multi-layer non-hydrostatic model to simulate breaking wave statistics, successfully reproducing observed distributions and scaling laws, and enabling advanced ocean turbulence studies.

Contribution

A novel multi-layer framework generalizing the Saint-Venant system to model wave breaking without overturning, matching empirical data and scaling laws.

Findings

Recovered the $ ext{Lambda}(c) o c^{-6}$ scaling for steep wave fields.

Modelled breaking distributions align with field measurements.

Scaling based on mean square slope and peak phase speed is effective.

Abstract

The statistics of breaking wave fields is characterised within a novel multi-layer framework, which generalises the single-layer Saint-Venant system into a multi-layer and non-hydrostatic formulation of the Navier-Stokes equations. We simulate an ensemble of phase-resolved surface wave fields in physical space, where strong non-linearities including wave breaking are modelled, without surface overturning. We extract the kinematics of wave breaking by identifying breaking fronts and their speed, for freely evolving wave fields initialised with typical wind wave spectra. The $\Lambda(c)$ distribution, defined as the length of breaking fronts (per unit area) moving with speed $c$ to $c+dc$ following Phillips 1985, is reported for a broad range of conditions. We recover the $\Lambda(c) \propto c^{-6}$ scaling without any explicit wind forcing for steep enough wave fields. A scaling of $\Lambda(c)$ based solely on the mean square slope and peak wave phase speed is shown to describe the modelled breaking distributions well. The modelled breaking distributions are found to be in good agreement with field measurements and the proposed scaling is consistent with previous empirical formulations. The present work paves the way for simulations of the turbulent upper ocean directly coupled with realistic breaking waves dynamics, including Langmuir turbulence, and other sub-mesoscale processes.