Blocking Spectra of Wind Waves

M. M. Zaslavskii

Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovskii pr. 36, Moscow, 117851 Russia

Received August 12, 1997; in final form, June 16, 1998

Abstract—For description of the small-scale region of the spectrum of wind waves, the concept of the “block-
ing” range is proposed in which the waves cease to take wind energy, and this energy is transferred to the surface
drift current through wave crest breaking. It is shown that the general phenomenological balance equation for
the spectrum of wind waves N(k) of the form dN/dt = P0 + P+ frame0 P frame1 yields two conditions P0 = 0 and P+ = P frame2 in
the blocking range. The first condition makes it possible to determine an explicit form of the wave spectrum
N
(k) in the blocking range from the nonlinear interaction term P0 = P0(N), and the second condition allows the
determination of the dissipation spectrum P frame3(k) in this range of scales. For weakly nonlinear waves, when P0(N)
is a four-wave nonlinear interaction term cubic in N, an explicit form of the blocking spectrum N(k) is found in
the directional approximation. In the strongly nonlinear limit, the blocking spectrum N(k) proves to be consis-
tent with the Phillips spectrum obtained for the saturation range from dimensional considerations.


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