Turbulence of capillary waves revisited

Abstract

Kinetic regime of capillary wave turbulence is classically regarded in terms of three-wave interactions with the exponent of power energy spectrum being $\nu =-7/4$ (two-dimensional case). We show that a number of assumptions necessary for this regime to occur can not be fulfilled. Four-wave interactions of capillary waves should be taken into account instead, which leads to exponents $\nu =-13/6$ and $\nu =-3/2$ for one- and two-dimensional wavevectors correspondingly. It follows that for general dispersion functions of decay type, three-wave kinetic regime need not prevail and higher order resonances may play a major role. Accepted for publication.

References in corpus (2)

• Mesoscopic wave turbulence
• Discrete Wave Turbulence