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Numerical simulation of the Benjamin-Feir instability and its consequences.
- Source :
-
Physics of Fluids . Jan2007, Vol. 19 Issue 1, p016602. 15p. 15 Graphs. - Publication Year :
- 2007
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10706631
- Volume :
- 19
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Physics of Fluids
- Publication Type :
- Academic Journal
- Accession number :
- 23923458
- Full Text :
- https://doi.org/10.1063/1.2432303