Energy spectra of \textbf{2D} gravity and capillary waves with narrow frequency band excitation

Abstract

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 ${ø}_0$ 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 $ø(k)\sim k^{1/2}$ and $ø(k)\sim k^{3/2}$ 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).

Submitted

References in corpus (3)

• Gravity surface wave turbulence in a laboratory flume
• Modulation instability and capillary wave turbulence
• Dynamical cascade generation as basic mechanism of Benjamin-Feir instability

Cited by in corpus (5)

• Inverse cascade of gravity waves in the presence of condensate: numerical simulation
• Energy transport in weakly nonlinear wave systems with narrow frequency band excitation
• Time scales and structures of wave interaction
• Direct dynamical energy cascade in the modified KdV equation
• Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation