JETP Letters

, Volume 97, Issue 4, pp 188–193 | Cite as

On the modulation instability of surface waves on a large-scale shear flow

  • V. P. Ruban
Plasma, Hydro- and Gas Dynamics


The problem of the modulation instability of a weakly nonlinear quasi-monochromatic wave on the surface of deep water in the presence of a steady-state collinear large-scale inhomogeneous flow (e.g., of a jet type) has been considered. In a certain range of (obtuse) angles of incidence of the wave with respect to the flow direction, the steepness of the refracted wave increases considerably, which contributes to the enhancement of nonlinear effects, including the formation of so-called rogue waves. The corresponding nonlinear Schrödinger equation with variable coefficients suitable for the analysis of the modulation instability has been derived.


Surface Wave JETP Letter Modulation Instability Rogue Wave Peregrine 
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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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