The instability of near-extreme Stokes waves

TL;DR

This paper investigates the stability of Stokes waves on an ideal fluid surface, revealing that steep waves are more prone to localized crest instabilities leading to breakers, contrasting with the modulational instability in small waves.

Contribution

It provides a detailed analysis of the instability mechanisms of Stokes waves, highlighting the dominance of localized crest disturbances in steep waves and their nonlinear evolution.

Findings

Localized crest disturbances dominate in steep waves

Steep waves tend to form plunging breakers

Small waves are primarily affected by modulational instability

Abstract

We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an instability due to disturbances localized at the wave crest, explaining why long propagating ocean swell consists of small-amplitude waves. The dominant localized disturbances are either co-periodic with the Stokes wave, or have twice its period. The nonlinear stage of instability for steep wave evolution reveals the formation of a plunging breaker.