TY - JOUR

T1 - Turbulence of capillary waves-theory and numerical simulation

AU - Pushkarev, A. N.

AU - Zakharov, V. E.

N1 - Funding Information:
This work was supported by the Office of Naval Research of the USA (grants N00 14-92-J-1343 and N000 14-98-1-0070) and partially by Russian Basic Research Foundation (grant 94-01-00898). We are using this opportunity to acknowledge these foundations.

PY - 1997

Y1 - 1997

N2 - An ensemble of weakly-interacting capillary waves on a free surface of deep ideal fluid is described statistically by the methods of weak turbulence. The stationary kinetic equation for capillary waves has an exact Kolmogorov solution which gives, for a spatial spectrum of elevations, asymptotics Ik = C (P 1/2 /σ3/4 k-19/4. The Kolmogorov constant C is found analytically together with the interval of locality in k̄-space. Direct numerical simulation of dynamical equations, in the small surface angles approximation, confirms the presence of an almost isotropic Kolmogorov spectrum in the large k̄ region. In the pumping region, the spectrum is defined by non-resonant processes of nonlinear damping. This fact can be explained by the narrowness of the inertial interval. Moreover, at small amplitudes of the pumping, an essentially new phenomenon is found: `frozen' turbulence, in which, despite the big number of interacting waves (of the order of 100) there is no energy flux toward high k̄. This phenomenon is connected with the finiteness of the region (or, in other words, the discreetness of the spectrum in Fourier space). This is believed to be universal for different sorts of nonlinear systems.

AB - An ensemble of weakly-interacting capillary waves on a free surface of deep ideal fluid is described statistically by the methods of weak turbulence. The stationary kinetic equation for capillary waves has an exact Kolmogorov solution which gives, for a spatial spectrum of elevations, asymptotics Ik = C (P 1/2 /σ3/4 k-19/4. The Kolmogorov constant C is found analytically together with the interval of locality in k̄-space. Direct numerical simulation of dynamical equations, in the small surface angles approximation, confirms the presence of an almost isotropic Kolmogorov spectrum in the large k̄ region. In the pumping region, the spectrum is defined by non-resonant processes of nonlinear damping. This fact can be explained by the narrowness of the inertial interval. Moreover, at small amplitudes of the pumping, an essentially new phenomenon is found: `frozen' turbulence, in which, despite the big number of interacting waves (of the order of 100) there is no energy flux toward high k̄. This phenomenon is connected with the finiteness of the region (or, in other words, the discreetness of the spectrum in Fourier space). This is believed to be universal for different sorts of nonlinear systems.

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M3 - Article

AN - SCOPUS:0031333116

SN - 0375-9474

VL - 17

SP - 111

EP - 131

JO - Unknown Journal

JF - Unknown Journal

ER -