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Weakly turbulent laws of wind-wave growth

Published online by Cambridge University Press:  30 October 2007

SERGEI I. BADULIN ,
ALEXANDER V. BABANIN ,
VLADIMIR E. ZAKHAROV  and
DONALD RESIO
SERGEI I. BADULIN
Affiliation:
P. P. Shirshov Institute of Oceanology of Russian Academy of Sciences Moscow, Russia
ALEXANDER V. BABANIN
Affiliation:
Swinburne University of Technology, Melbourne, Australia
VLADIMIR E. ZAKHAROV
Affiliation:
Waves and Solitons LLC, Phoenix, Arizona, USA P. N. Lebedev Physical Institute of Russian Academy of Sciences, Moscow, Russia University of Arizona, Tuscon, USA
DONALD RESIO
Affiliation:
Waterways Experiment Station, USA, Vicksburg, Massachusetts, USA
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Abstract

The theory of weak turbulence developed for wind-driven waves in theoretical works and in recent extensive numerical studies concludes that non-dimensional features of self-similar wave growth (i.e. wave energy and characteristic frequency) have to be scaled by internal wave-field properties (fluxes of energy, momentum or wave action) rather than by external attributes (e.g. wind speed) which have been widely adopted since the 1960s. Based on the hypothesis of dominant nonlinear transfer, an asymptotic weakly turbulent relation for the total energy ϵ and a characteristic wave frequency ω* was derived The self-similarity parameter αss was found in the numerical duration-limited experiments and was shown to be naturally varying in a relatively narrow range, being dependent on the energy growth rate only.

In this work, the analytical and numerical conclusions are further verified by means of known field dependencies for wave energy growth and peak frequency downshift. A comprehensive set of more than 20 such dependencies, obtained over almost 50 years of field observations, is analysed. The estimates give αss very close to the numerical values. They demonstrate that the weakly turbulent law has a general value and describes the wave evolution well, apart from the earliest and full wave development stages when nonlinear transfer competes with wave input and dissipation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 591 , 25 November 2007 , pp. 339 - 378
Copyright
Copyright © Cambridge University Press 2007

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