A SIMPLE THEORY OF CAPILLARY-GRAVITY WAVE TURBULENCE

Employing a recently proposed 'multi-wave interaction' theory (Glazman 1992), inertial spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a co mplicated dispersion law. The absence of scale invariance makes this a nd some other problems of wave turbulence (e.g. nonlinear inertia-grav ity waves) intractable by small-perturbation techniques, even in the w eak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasona ble agreement with experimental data. The theory explains the dependen ce of the wave spectrum on wind input and describes the accelerated ro ll-off of the spectral density function in the narrow sub-range separa ting scale-invariant regimes of purely gravity and capillary waves, wh ile the appropriate (long- and short-wave) limits yield power laws cor responding to the Zakharov-Filonenko and Phillips spectra.