Resonant sloshing in shallow water

DOI10.1017/S0022112086002926zbMath0607.76037MaRDI QIDQ3747093

Andrew Johnson, Hilary Ockendon, John R. Ockendon

Publication date: 1986

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

zbMATH Keywords

dissipationdispersionmultiple solutionsAsymptotic methodsresonanceshallow waterdetuning parametershallow-water sloshingforced water waves

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) Basic methods in fluid mechanics (76M99)

Related Items (21)

Asymptotic nonlinear multimodal modeling of liquid sloshing in an upright circular cylindrical tank. I: Modal equations ⋮ Higher-order Melnikov theory for adiabatic systems ⋮ Two-dimensional modal method for shallow-water sloshing in rectangular basins ⋮ A rigorous proof of an exponentially small estimate for a boundary value arising from an ordinary differential equation ⋮ A geometric criterion for adiabatic chaos ⋮ Modulation theory for the steady forced KdV-Burgers equation and the construction of periodic solutions ⋮ Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in two dimensions ⋮ Uniform asymptotic expansions of solutions of an inhomogeneous equation ⋮ Linear sloshing frequencies in the annular region of a circular cylindrical container in the presence of a rigid baffle ⋮ Travelling-wave spatially periodic forcing of asymmetric binary mixtures ⋮ On the Solutions of a Second Order Differential Equation Arising in the Theory of Resonant Oscillations in a Tank ⋮ On chaotic wave patterns in periodically forced steady-state KdVB and extended KdVB equations ⋮ Unifying the steady state resonant solutions of the periodically forced KdVB, mKdVB, and eKdVB equations ⋮ A differential equation in the theory of resonant oscillations of water waves ⋮ Dynamic coupling between shallow-water sloshing and horizontal vehicle motion ⋮ Steady free-surface flow over spatially periodic topography ⋮ Solutions of slowly and periodically varying differential equations. Applications to some classical examples ⋮ The Asymptotic Solution of a Connection Problem of a Second Order Ordinary Differential Equation ⋮ Use of simple shooting to obtain chaos ⋮ A shooting approach to layers and chaos in a forced Duffing equation ⋮ On the periodic solutions of a forced second-order equation

Cites Work

• The evolution of resonant oscillations in closed tubes
• Asymptotic solutions of nonlinear second order differential equations with variable coefficients
• Slowly Varying Phase Planes and Boundary-Layer Theory
• Resonant surface waves
• Resonant oscillations in closed tubes

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