Recurrent solutions of Alber's equation for random water-wave fields
Authors:
- 25 February 2008
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 598, 245-266
Abstract
The study addresses the linear instability of narrow spectra homogeneous seas and its subsequent evolution in time, subject to inhomogeneous disturbances. Specifically, we study unidirectional spectra, where according to the kinetic equation no spectral evolution is expected. In the region of instability, recurrent evolution is discovered. This recurrence is the stochastic counterpart of the Fermi–Pasta–Ulam recurrence obtained for the cubic Schrödinger equation.Keywords
This publication has 12 references indexed in Scilit:
- Modulational instability of nonlinearly interacting incoherent sea statesJETP Letters, 2007
- Nonlinear Four-Wave Interactions and Freak WavesJournal of Physical Oceanography, 2003
- Evolution of a narrow-band spectrum of random surface gravity wavesJournal of Fluid Mechanics, 2003
- Dynamics and Modelling of Ocean Waves1994
- Long-time evolution of an unstable water-wave trainJournal of Fluid Mechanics, 1982
- Evolution of a random inhomogeneous field of nonlinear deep-water gravity wavesWave Motion, 1980
- The effects of randomness on the stability of two-dimensional surface wavetrainsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1978
- Relationship between Benjamin–Feir instability and recurrence in the nonlinear Schrödinger equationThe Physics of Fluids, 1978
- Stability of periodic waves of finite amplitude on the surface of a deep fluidJournal of Applied Mechanics and Technical Physics, 1968
- On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theoryJournal of Fluid Mechanics, 1962