Ya. V. Saprykinaa, S. Yu. Kuznetsova, Zh. Chernevab, and N. Andreevab
a Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia
b Nansen Institute of Oceanology “Fridtj of Nansen”, Bulgarian Academy of Sciences, Varna, Bulgaria
E-mail: saprykina@ocean.ru, kuznetsov@ocean.ru, cherneva@io-bas.bg, n.andreeva@io-bas.bg
Received July 11, 2008; in final form, October 8, 2008
Abstract—The spatio-temporal variability of individual storm waves in the coastal zone is studied. Wave chro-
nograms were presented as sums of the first and second harmonics with amplitudes slowly varying in time,
which are envelopes for the waves of the corresponding frequency bands. The amplitude-frequency structure of
individual waves was estimated from the variations in the amplitude of the envelopes. Bi-spectral analysis was
applied to estimate the phase composition of the waves. It is shown that, in the initial stage of transformation,
the fluctuations of the waves of the first and second harmonics are synchronous. The amplitudes of the second
harmonics are proportional to the squared amplitudes of the first harmonics. Thus, a simple model is possible
for the description of individual waves based, for example, on the generalization of the Stokes theory. As the
waves approach the coast, the ratio of the amplitudes of the first and second harmonics in individual waves var-
ies in time chaotically, thus it is not possible to describe individual waves on the basis of a simple model. The
main cause of the chaotic variation of the amplitudes is the backward transfer of energy from the highest har-
monics to the first harmonics due to the sub-near resonant triad interaction close to the resonance. The phase
composition of individual waves depends on the distance propagated by the waves and on the stage (main or
backward) of the energy exchange between the nonlinear harmonics.
DOI: 10.1134/S0001437009020039
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