Physics – Fluid Dynamics
Scientific paper
2011-07-13
EPL, 97 (2012) 30004
Physics
Fluid Dynamics
Submitted
Scientific paper
10.1209/0295-5075/97/30004
In this Letter we present a new method, called chain equation method (CEM), for computing a cascade of distinct modes in a two-dimensional weakly nonlinear wave system generated by narrow frequency band excitation. The CEM is a means for computing the quantized energy spectrum as an explicit function of frequency $\o_0$ and stationary amplitude $A_0$ of excitation. The physical mechanism behind the generation of the quantized cascade is modulation instability. The CEM can be used in numerous \textbf{2D} weakly nonlinear wave systems with narrow frequency band excitation appearing in hydrodynamics, nonlinear optics, electrodynamics, convection theory etc. In this Letter the CEM is demonstrated with examples of gravity and capillary waves with dispersion functions $\o(k) \sim k^{1/2}$ and $\o(k) \sim k^{3/2}$ respectively, and for two different levels of nonlinearity $\eps=A_0k_0$: small ($\eps\sim 0.1$ to 0.25) and moderate ($\eps\sim 0.25$ to 0.4).
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