Contribution of Forced Harmonics Into Wind Wave Spectra

Basic equations of weakly nonlinear theory of water waves are written in special vari- ables that are related to original physical variables through a nonlinear transformation. The transformation takes into account an effect of forced harmonics -- corrections to linear theory solutions. This fact is usually ignored in a great number of studies, the nonlinear corrections are considered as vanishingly small for sea wave conditions. In the present work the problem of the transformation from "canonical" to "observed" wave spectra is discussed in the context of kinetic equation for water waves. The ef- fect is specified for model and calculated spectra in deep and shallow water cases. The effect is shown to be significant just in deep water case due to its integral nature and features of water wave spectra -- sharp peak with rather low background in high and low frequencies. For the background these corrections, or, in other words, the forced harmonics contribution can exceed zero-order values. The problem of experimental discrimination of master (zero-order) and forced harmonics contribution is discussed.

The research was conducted under the U.S. Army Corps of Engineers, RDT&E pro- gram, grant DACA 42-00-C0044, ONR grant N00014-98-1-0070 and Russian Foun- dation for Basic Research grants N01-05-64603, N01-05-64464.