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The dominant instability of near-extreme Stokes waves
Bernard Deconinck1, Sergey A Dyachenko2, Pavel M Lushnikov3
1Department of Applied Mathematics, University of Washington, Seattle, WA 98195-3925.
Summary
For steeper waves, localized disturbances at wave crests cause instabilities that lead to plunging breakers, explaining ocean swell dynamics. This contrasts with small amplitude waves dominated by Benjamin-Feir instability.
Area of Science:
- Fluid dynamics
- Nonlinear science
- Wave propagation
Background:
- Stokes waves are fundamental to understanding nonlinear wave phenomena.
- Wave train dynamics are typically dominated by Benjamin-Feir instability for small amplitude waves.
Purpose of the Study:
- Investigate the dominant instability of Stokes waves based on wave steepness.
- Explain the formation of plunging breakers and ocean swell characteristics.
Main Methods:
- Analysis of wave instabilities in ideal fluids of infinite depth.
- Comparison of growth rates for different types of wave disturbances.
Main Results:
- For steeper Stokes waves, localized crest disturbances exhibit significantly higher growth rates than modulational instability.
- These dominant instabilities, coperiodic or twice the wave period, lead to plunging breaker formation.
Conclusions:
- Localized crest disturbances are the primary drivers of instability in steeper Stokes waves.
- This mechanism explains the prevalence of small-amplitude waves in long ocean swell.
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