Three-dimensional instabilities of nonlinear gravity-capillary waves

DOI10.1017/S0022112087000090zbMath0607.76035MaRDI QIDQ3747091

Jun Zhang, W. K. Melville

Publication date: 1987

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

zbMATH Keywords

Galerkin methodnumerical methodsbifurcationstability problemresonance curvesweakly nonlinear wavestriad resonanceseigenvalue systemthree-dimensional wavessteep wavesLinear three-dimensional instabilitiesnonlinear two-dimensional uniform gravity-capillary wavessuperharmonic two-dimensional instability

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Interfacial stability and instability in hydrodynamic stability (76E17) Hydrodynamic stability (76E99) Bifurcations in context of PDEs (35B32) Basic methods in fluid mechanics (76M99)

Related Items (15)

Linear stability of finite-amplitude capillary waves on water of infinite depth ⋮ Further results on the stability of symmetric and asymmetric resonant capillary-gravity waves ⋮ Thermocapillary stabilization of the capillary breakup of an annular film of liquid ⋮ Standing gravity waves of large amplitude in deep water ⋮ On the stability of gravity waves on deep water ⋮ Evolution equations which model the ripples arising from an adjacent mode interaction ⋮ Transverse dynamics of two-dimensional traveling periodic gravity-capillary water waves ⋮ FIFTH-ORDER EVOLUTION EQUATION OF GRAVITY–CAPILLARY WAVES ⋮ On the observability of finite-depth short-crested water waves ⋮ On the disappearance of the lowest-order instability for steep gravity waves in finite depth ⋮ Nonlinear stability of resonant capillary-gravity waves ⋮ Gravity–capillary multi-component wave patterns generated by a single-frequency wave-maker oscillation and subsequent resonances ⋮ Finite-amplitude steady-state wave groups with multiple near-resonances in finite water depth ⋮ Numerical simulations of the quasi-stationary stage of ripple excitation by steep gravity–capillary waves ⋮ Stability analysis of deep-water waves on a linear shear current using unsteady conformal mapping

Cites Work

• Three-Dimensional Stability and Bifurcation of Capillary and Gravity Waves on Deep Water
• Some effects of surface tension on steep water waves. Part 2
• Some effects of surface tension on steep water waves. Part 3
• Instabilities of finite-amplitude water waves
• On two-dimensional packets of capillary-gravity waves
• Significant Interactions Between Small and Large Scale Surface Waves
• Computer extension and analytic continuation of Stokes’ expansion for gravity waves
• The disintegration of wave trains on deep water Part 1. Theory
• A criterion for nonlinear wave stability

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