Self-similarity of wind-driven seas and universality of wind wave growth
Date/Time: 12:20 06-Aug-2014
For wind-driven growing waves we found a simple universal relationship that relates the instant wave steepness with the number of waves appeared since the beginning of the process of wave development. The relationship holds both in fetch and duration domains and does not contain wind-sea interaction parameters explicitly. It relies upon recent advances of the theory of weak turbulence of water waves where wave nonlinearity is assumed to be a leading physical mechanism.
Self-similar solutions as reference cases of the theory are generalized for arbitrary rates of wave growth by developing a simple adiabatic approach where fetch and duration become key physical scales replacing habitual wind speed scaling. With the new scaling the dependencies of non-dimensional wave height on non-dimensional wave period are universal power-law functions with exponents $5/2$ (fetch-limited case) and $9/4$ (duration-limited).
The validity of the proposed theory is illustrated by results of numerical simulations, in situ measurements of growing wind seas and wind-wave tank experiments. The impact of the new vision of sea wave physics is discussed in the context of conventional approaches to wave modeling and forecasting.
|© 2012, Landau Institute for Theoretical Physics RAS www.itp.ac.ru