Turbulence of capillary waves - theory and numerical simulation

An ensemble of weakly interacting capillary waves on a free surface of deep ideal fluid is described statistically by methods of weak turbulence. The stationary kinetic equations for capillary waves have an exact Kolmogorov s olution which gives for the spatial spectrum of elevations asymptotics I-k = C(P-1/2 / sigma(3/4))k(-19/4). The Kolmogorov constant C is found analyti cally together with the interval of locality in (K) over right arrow -space . Direct numerical simulation of the dynamical equations in the approximati on of small surface angles confirms the presence of almost istropic Kolmogo rov spectrum in the large k region. Besides, at (k) over right arrow small amplitudes of the pumping, an esentially new phenomenon is found: "frozen" turbulence, in which, despite the big number of interacting waves (of the o rder of 100) there is no energy flux toward high (k) over right arrow. This phenomenon is connected with the finiteness of the region (or, in other wo rds, discreteness of the spectrum in Fourier space). This is believed to be universal for different sorts of nonlinear systems. (C) 2000 Elsevier Scie nce B.V. All rights reserved.