Subharmonic resonance of nonlinear cross-waves
- 1 October 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 183, 451-465
- https://doi.org/10.1017/s0022112087002726
Abstract
The evolution equation governing wavemaker-generated cross-waves near a cutoff frequency in an infinitely deep, infinitely long channel is shown to be the nonlinear Schrödinger equation with a homogeneous boundary condition at the wavemaker. With the inclusion of an empirically determined damping coefficient, numerical results for growth rate, slow modulation period, and wave amplitude show good agreement with previous experiments. The results also describe observations of trapped and propagating solutions.Keywords
This publication has 11 references indexed in Scilit:
- Experiments on nonlinear cross wavesPhysics of Fluids, 1986
- Chaotic mode competition in parametrically forced surface wavesJournal of Fluid Mechanics, 1985
- Note on a parametrically excited, trapped cross-waveJournal of Fluid Mechanics, 1985
- Parametrically excited solitary wavesJournal of Fluid Mechanics, 1984
- Observation of a Nonpropagating Hydrodynamic SolitonPhysical Review Letters, 1984
- The generation of cross-waves in a long deep channel by parametric resonanceJournal of Fluid Mechanics, 1984
- Nonlinear waves near a cut-off frequency in an acoustic duct – a numerical studyJournal of Fluid Mechanics, 1982
- Cross-waves. Part 2. ExperimentsJournal of Fluid Mechanics, 1972
- Cross-waves. Part 1. TheoryJournal of Fluid Mechanics, 1972
- On cross-wavesJournal of Fluid Mechanics, 1970