On the modulational stability of traveling and standing water waves

DOI10.1063/1.868288zbMath0830.76013OpenAlexW2023961295MaRDI QIDQ4838741

Robert D. Pierce, Edgar Knoblauch

Publication date: 12 July 1995

Published in: Physics of Fluids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.868288

zbMATH Keywords

capillary-gravity wavesfluid depthsmall amplitude counterpropagating waves

Mathematics Subject Classification ID

Nonlinear effects in hydrodynamic stability (76E30) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45)

Related Items (13)

Asymptotically exact Zakharov equations and the stability of water waves with bimodal spectra ⋮ Fourth-order nonlinear evolution equations for a capillary-gravity wave packet in the presence of another wave packet in deep water ⋮ Nonlinear evolution equations in crossing seas in the presence of uniform wind flow ⋮ Nonlinear evolution equations of co-propagating waves over finite depth fluid ⋮ Justification of mean-field coupled modulation equations ⋮ Water waves in a deep square basin ⋮ Dynamics of counterpropagating waves in parametrically forced systems ⋮ Interaction of two quasi-monochromatic waves in shallow water ⋮ Modulational stability of travelling waves in 2D anisotropic systems ⋮ Nearly inviscid Faraday waves in annular containers of moderately large aspect ratio ⋮ Stability of capillary–gravity interfacial waves between two bounded fluids ⋮ The 1:2 resonance with \(O(2)\) symmetry and its applications in hydrodynamics ⋮ Stability of bichromatic gravity waves on deep water

Cites Work

• Nonlinear and nonlocal dynamics of spatially extended systems: Stationary states, bifurcations and stability
• On the evolution of packets of water waves
• An analysis of two-dimensional water waves based on O(2) symmetry
• Stability of weakly nonlinear deep-water waves in two and three dimensions
• Standing waves in deep water: Their stability and extreme form
• On two-dimensional packets of capillary-gravity waves
• On three-dimensional packets of surface waves
• On Wilton's ripples: a special case of resonant interactions
• Standing capillary-gravity waves of finite amplitude
• Amplitude equations for travelling wave convection

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