Secondary bifurcation and change of type for three-dimensional standing waves in finite depth

DOI10.1017/S0022112087001460zbMath0635.76009OpenAlexW2111337609MaRDI QIDQ3775155

Thomas J. Bridges

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1017/s0022112087001460

zbMATH Keywords

periodic solutionseigenvaluessurface wavesirrotational water wavesrectangular cross- sectionexchange of energynonlinear periodic free oscillationssecondary bifurcation of periodic solutionsStrong internal resonancethree-dimensional basinthree-dimensional cnoidal standing waves

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Partial differential equations of mathematical physics and other areas of application (35Q99) Bifurcations in context of PDEs (35B32)

Related Items

Computation of three-dimensional standing water waves ⋮ Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank ⋮ Symmetry-breaking bifurcations in resonant surface waves ⋮ MODAL MODELLING OF THE NONLINEAR RESONANT FLUID SLOSHING IN A RECTANGULAR TANK I: A SINGLE-DOMINANT MODEL ⋮ Autoparametric interaction of a liquid surface in a rectangular tank with an elastic support structure under 1:1 internal resonance ⋮ Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

Cites Work

• On the evolution of packets of water waves
• Theta functions and non-linear equations
• Cascading Bifurcations
• Internally resonant surface waves in a circular cylinder
• Resonantly forced surface waves in a circular cylinder
• An Analytical Model of Periodic Waves in Shallow Water
• Cnoidal standing waves and the transition to the traveling hydraulic jump
• On the Secondary Bifurcation of Three-Dimensional Standing Waves
• Secondary States of Rectangular Plates
• New magnetohydrodynamic equilibria by secondary bifurcation
• Three-Dimensional Standing Surface Waves of Finite Amplitude

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