Numerical simulation of the Benjamin-Feir instability and its consequences

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Title: Numerical simulation of the Benjamin-Feir instability and its consequences
Author(s): Chalikov, Dmitry
Abstract: Full nonlinear equations for one-dimensional potential surface waves were used for investigation of the evolution of an initially homogeneous train of exact Stokes waves with steepness AK=0.01-0.42. The numerical algorithm for the integration of nonstationary equations and the calculation of exact Stokes waves is described. Since the instability of the exact Stokes waves develops slowly, a random small-amplitude noise was introduced in initial conditions. The development of instability occurs in two stages: in the first stage the growth rate of disturbances was close to that established for small steepness by Benjamin and Feir [J. Fluid. Mech. 27, 417 (1967)] and for medium steepness [McLean, J. Fluid Mech. 114, 315 (1982)]. For any steepness, the Stokes waves disintegrate and create random superposition of waves. For AK<0.13, waves do not show a tendency to breaking, which is recognized by approaching a surface to non-single-value shape. Sooner or later, if AK>0.13, one of the waves increases its height, and finally it comes to the breaking point. For large steepness of AK>0.35 the rate of growth is slower than for medium steepness. The data for spectral composition of disturbances and their frequencies are given.
Publication type: Journal article
Source: Physics of Fluids, Vol. 19, no. 1 (Jan 2007), paper no. 016602
Publication year: 2007
FOR Code(s): 0102 Applied Mathematics; 0203 Classical Physics; 0915 Interdisciplinary Engineering
Keyword(s): Algorithms; Benjamin-Feir instability; Computer simulation; Flow instability; Flow measurement; Flow of fluids; Flow simulation; Integration; Nonlinear equations; Random noise; Random processes; Surface waves
Publisher: American Institute of Physics
ISSN: 1070-6631
Publisher URL: http://dx.doi.org/10.1063/1.2432303
Peer reviewed