Instabilities of finite-amplitude water waves

1982/01/01 by J. McLean · 243 citations
Earth and Planetary Sciences · #Ocean Waves and Remote Sensing #Coastal and Marine Dynamics #Oceanographic and Atmospheric Processes #Amplitude #Instability #Physics #Dispersion relation #Perturbation (astronomy) #Mechanics #Wavenumber #Classical mechanics #Optics

paper · doi:10.1017/s0022112082000172

published in Journal of Fluid Mechanics 114, 315-330 (Cambridge University Press)

openalex publication_date 1982/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A numerical investigation of normal-mode perturbations of a finite-amplitude Stokes wave has revealed regions of instability lying near resonance curves given by the linear-dispersion relation. It is found that, for small amplitude, the dominant instability is two-dimensional (of Benjamin-Fier type) but, for larger amplitudes, the dominant instability becomes a three-dimensional perturbation. Results are compared with recent experimental observations of steep wave trains.

Citations

• Computer extension and analytic continuation of Stokes’ expansion for gravity waves
• Stability of periodic waves of finite amplitude on the surface of a deep fluid
• The disintegration of wave trains on deep water Part 1. Theory

Cited by

• NONLINEAR GRAVITY AND CAPILLARY-GRAVITY WAVES
• Stokes wave [wikipedia]