Long-time behaviour of a random inhomogeneous field of weakly nonlinear surface gravity waves

DOI10.1017/S0022112083001810zbMath0543.76027OpenAlexW2146018522MaRDI QIDQ3332531

Peter A. E. M. Janssen

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1017/s0022112083001810

zbMATH Keywords

nonlinear Schrödinger equationlong-time behaviourhomogeneous spectrumGaussian randomnonlinear interaction of wave trainsrandom inhomogeneous fieldspectral growth

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stochastic analysis applied to problems in fluid mechanics (76M35)

Related Items (5)

Statistical approach of modulational instability in the class of derivative nonlinear Schrödinger equations ⋮ Evolution of statistically inhomogeneous degenerate water wave quartets ⋮ Recurrent solutions of Alber's equation for random water-wave fields ⋮ What makes the Peregrine soliton so special as a prototype of freak waves? ⋮ A transport equation for flexural-gravity wave propagation under a sea ice cover of variable thickness

Cites Work

• Plasma oscillations
• Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves
• On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions
• On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory
• Limit cycle behavior of the bump-on-tail instability
• Modulational instability and the Fermi-Pasta-Ulam recurrence
• Energy transport in a nonlinear and inhomogeneous random gravity wave field
• On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model
• A transport-equation description of nonlinear ocean surface wave interactions
• On the Quantum Correction For Thermodynamic Equilibrium
• The disintegration of wave trains on deep water Part 1. Theory
• Kelvin–Helmholtz instability of finite amplitude
• Nonlinear waves in a Kelvin-Helmholtz flow
• On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility

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