Small amplitude capillary-gravity waves in a channel of finite depth

DOI10.1017/S0017089500007667zbMath0683.76019MaRDI QIDQ4733552

Mark C. W. Jones

Publication date: 1989

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

theory of bifurcationhorizontal bottominfinite depth problemhorizontal laminar flow with flat free surfacenew integral equationperiodic capillary-gravity wave problemsteady, two-dimensional, symmetric waves

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30)

Related Items (12)

Global bifurcation for water waves with capillary effects and constant vorticity ⋮ Modulational instability in the Whitham equation with surface tension and vorticity ⋮ Periodic capillary-gravity water waves of small amplitude ⋮ Stratified periodic water waves with singular density gradients ⋮ Equatorial wind waves with capillary effects and stagnation points ⋮ Existence of capillary-gravity water waves with piecewise constant vorticity ⋮ On 1:2 resonant waves which arise between two stratified fluids of finite vertical extent in the presence of mean flow effects ⋮ Steady periodic water waves with unbounded vorticity: equivalent formulations and existence results ⋮ An existence theory for three-dimensional periodic travelling gravity-capillary water waves with bounded transverse profiles ⋮ Capillary-gravity water waves with discontinuous vorticity: existence and regularity results ⋮ Modulational instability in a full‐dispersion shallow water model ⋮ Trimodal steady water waves

Cites Work

• Singularities and groups in bifurcation theory. Volume I
• On Wilton ripples. I: Formal derivation of the phenomenon
• Symmetry and the bifurcation of capillary-gravity waves
• Bifurcation from simple eigenvalues
• Solitary and periodic gravity—capillary waves of finite amplitude
• The bifurcation and secondary bifurcation of capillary-gravity waves
• Steady Gravity-Capillary Waves On Deep Water-1. Weakly Nonlinear Waves
• Secondary Bifurcation Near a Double Eigenvalue
• Some effects of surface tension on steep water waves
• Nonlinear periodic capillary-gravity waves on a fluid of finite depth
• Finite amplitude surface waves in a liquid layer

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