Direct and Inverse Cascades in the WindDriven Sea
Abstract
We offer a new form for the S(nl) term in the Hasselmann kinetic equation for squared wave amplitudes of winddriven gravity wave. This form of S(nl) makes possible to rewrite in differential form the conservation laws for energy, momentum, and wave action, and introduce their fluxes by a natural way. We show that the stationary kinetic equation has a family of exact Kolmogorovtype solutions governed by the fluxes of motion constants: wave action, energy, and momentum. The simple "local" model for S(nl) term that is equivalent to the "diffusion approximation" is studied in details. In this case, Kolmogorov spectra are found in the explicit form. We show that a general solution of the stationary kinetic equation behind the spectral peak is described by the Kolmogorovtype solution with frequencydependent fluxes. The domains of "inverse cascade" and "direct cascade" can be separated by natural way. The spectrum in the universal domain is close to $\omega^{4}$.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 DOI:
 10.48550/arXiv.1502.02628
 arXiv:
 arXiv:1502.02628
 Bibcode:
 2015arXiv150202628Z
 Keywords:

 Physics  Atmospheric and Oceanic Physics;
 Physics  Fluid Dynamics