Rogue Waves and Modulational Instability
Abstract
The most plausible cause of rogue wave formation in a deep ocean is development of modulational instability of quasimonochromatic wave trains. An adequate model for study of this phenomenon is the Euler equation for potential flow of incompressible fluid with free surface in 2-D geometry. Numerical integration of these equations confirms completely the conjecture of rogue wave formation from modulational instability but the procedure is time consuming for determination of rogue wave appearance probability for a given shape of wave energy spectrum. This program can be realized in framework of simpler model using replacement of the exact interaction Hamiltonian by more compact Hamiltonian. There is a family of such models. The popular one is the Nonlinear Schrodinger equation (NLSE). This model is completely integrable and suitable for numerical simulation but we consider that it is oversimplified. It misses such important phenomenon as wave breaking. Recently, we elaborated much more reliable model that describes wave breaking but is as suitable as NLSE from the point of numerical modeling. This model allows to perform massive numerical experiments and study statistics of rogue wave formation in details.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2015
- Bibcode:
- 2015AGUFMNG32A..08Z
- Keywords:
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- 3389 Tides and planetary waves;
- ATMOSPHERIC PROCESSES;
- 2483 Wave/particle interactions;
- IONOSPHERE;
- 4455 Nonlinear waves;
- shock waves;
- solitons;
- NONLINEAR GEOPHYSICS