Nonlinearity and nonequilibrium together in Nature: wind waves in the open ocean
Department of Mathematics, University of Arizona,
2 Institut des Sciences Moléculaires d’Orsay ISMO-CNRS, Université Paris-Sud, Bt. 210, 91405 Orsay Cedex, France
a e-mail: firstname.lastname@example.org
Published online: 5 November 2010
We derive scaling laws for the steady spectrum of wind excited waves, neglecting surface tension and taking air and water as inviscid, an approximation valid at large wind speed. Independently of the wind speed, there exists an unique (small) dimensionless parameter ϵ, the ratio of the mass densities of the two fluids (air and water). The smallness of ϵ allows to derive some important average properties of the wave system. The average square slope of the waves is, as observed, a small but not very small quantity, because it is of order |ln(ϵ2)|-1. This supports the often used assumption of small nonlinearity in the wave-wave interaction. We introduce an equation to be satisfied by the two-point correlation of the height fluctuations. Lastly we reconsider the formation of swell, that is the relationship between the randomness of waves and the observation of quasi monochromatic water waves.
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2010