Nonlinear dynamics of trapped waves on jet currents and rogue waves
arXiv:1401.4455 · doi:10.1103/PhysRevE.89.041002
Abstract
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of (V. Shrira, A. Slunyaev, J. Fluid. Mech, 738, 65, 2014) leads to the one-dimensional modified nonlinear Schrödinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions in form of the modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
4 pages, 2 figures, 3 movies (supplemental materials, not enclosed to this submission)
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Cited by in corpus (5)
- Wave amplification in the framework of forced nonlinear Schrodinger equation: the rogue wave context
- Statistics of weakly nonlinear waves on currents with strong vertical shear
- Transformation of envelope solitons on a bottom step
- Deep water gravity wave triad resonances on uniform flow
- Coastal wave refraction in variable currents over a varying bathymetry