Bifurcation in gravity waves

DOI10.1017/S0022112085001057zbMath0575.76025OpenAlexW1992398314MaRDI QIDQ3694854

Michael S. Longuet-Higgins

Publication date: 1985

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0022112085001057

zbMATH Keywords

Asymmetric bifurcationsbifurcation of uniform wavescritical value of the wave steepness for the symmetric bifurcationscubic potential functiongravity waves on deep waterquadratic identities between Fourier coefficients in Stokes expansionseries of steady waves of non-uniform amplitude

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hydrodynamic stability (76E99)

Related Items (18)

Uniformly travelling water waves from a dynamical systems viewpoint: some insights into bifurcations from Stokes’ family ⋮ On the stability of gravity waves on deep water ⋮ Weakly nonlinear non-symmetric gravity waves on water of finite depth ⋮ Lagrangian moments and mass transport in Stokes waves ⋮ Non-symmetric gravity waves on water of infinite depth ⋮ Quasiperiodic perturbations of Stokes waves: secondary bifurcations and stability ⋮ Surfing surface gravity waves ⋮ Theory of deep-water surface gravity waves derived from a Lagrangian ⋮ Oscillatory spatially periodic weakly nonlinear gravity waves on deep water ⋮ Babenko's equation for periodic gravity waves on water of finite depth: derivation and numerical solution ⋮ Lagrangian moments and mass transport in Stokes waves Part 2. Water of finite depth ⋮ Accurate calculations of Stokes water waves of large amplitude ⋮ Accurate series solutions for gravity-driven Stokes waves ⋮ Influence of wind on extreme wave events: experimental and numerical approaches ⋮ A Lagrangian for water waves ⋮ A new limiting form for steady periodic gravity waves with surface tension on deep water ⋮ A Comparison of Nonlinear Water Wave Models ⋮ The propagation of short surface waves on longer gravity waves

Cites Work

• Numerical Evidence for the Existence of New Types of Gravity Waves of Permanent Form on Deep Water
• Theory of the almost-highest wave. Part 2. Matching and analytic extension
• Computer extension and analytic continuation of Stokes’ expansion for gravity waves

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