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.
