Verification of the Benjamin–Lighthill conjecture about steady water waves

DOI10.1017/S0022112095001996zbMath0852.76011WikidataQ123012203 ScholiaQ123012203MaRDI QIDQ4879242

Brooke Benjamin

Publication date: 12 December 1996

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

zbMATH Keywords

Hamiltonian representationsflow-force invariantinfinitely deep ideal liquidperiodic Stokes waves

Mathematics Subject Classification ID

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

Related Items (21)

Fundamental bounds for steady water waves ⋮ Global bifurcation and highest waves on water of finite depth ⋮ On the Benjamin–Lighthill conjecture for water waves with vorticity ⋮ Exact Travelling Periodic Water Waves in Two-Dimensional Irrotational Flows ⋮ On steady non-breaking downstream waves and the wave resistance – Stokes’ method ⋮ Babenko's equation for periodic gravity waves on water of finite depth: derivation and numerical solution ⋮ Bounds for steady water waves with vorticity ⋮ On the Hamiltonian structure of the planar steady water-wave problem with vorticity ⋮ The bifurcation of steady gravity water waves in (R, S) parameter space ⋮ Dispersion equation for water waves with vorticity and Stokes waves on flows with counter-currents ⋮ On behaviour of free-surface profiles for bounded steady water waves ⋮ Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity ⋮ Qualitative theory of nonlinear steady water waves ⋮ No steady water waves of small amplitude are supported by a shear flow with a still free surface ⋮ Fully nonlinear periodic internal waves in a two-fluid system of finite depth ⋮ The Benjamin-Lighthill conjecture for steady water waves (revisited) ⋮ On bounds for steady waves with negative vorticity ⋮ The Benjamin-Lighthill conjecture for near-critical values of Bernoulli's constant ⋮ On steady non-breaking downstream waves and the wave resistance ⋮ On the amplitude and the flow force constant of steady water waves ⋮ Steady water waves with vorticity: spatial Hamiltonian structure

Cites Work

• On solitary water-waves of finite amplitude
• Some new gravity waves in water of finite depth
• The Froude number for solitary waves
• Numerical Evidence for the Existence of New Types of Gravity Waves of Permanent Form on Deep Water
• On the theory of steady-state waves of finite amplitude

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