Advances in Geosciences www.adv-geosci.net 1680-7340 1680-7359 15 Topics in modern geophysical fluid dynamics 2008 10.5194/adgeo-15-35-2008 http://www.adv-geosci.net/15/35/2008/ http://www.adv-geosci.net/15/35/2008/adgeo-15-35-2008.html http://www.adv-geosci.net/15/35/2008/adgeo-15-35-2008.pdf 35 45 2008-05-13 Turbulent wind waves on a water current M. V. Zavolgensky P. B. Rutkevich peter@d902.iki.rssi.ru Water problems Institute RAN (IVP RAN ZD), Rostov-on-Don, Russia Space Research Institute (IKI), Moscow, Russia An analytical model of water waves generated by the wind over the water surface is presented. A simple modeling method of wind waves is described based on waves lengths diagram, azimuthal hodograph of waves velocities and others. Properties of the generated waves are described. The wave length and wave velocity are obtained as functions on azimuth of wave propagation and growth rate. Motionless waves dynamically trapped into the general picture of three dimensional waves are described. The gravitation force does not enter the three dimensional of turbulent wind waves. That is why these waves have turbulent and not gravitational nature. The Langmuir stripes are naturally modeled and existence of the rogue waves is theoretically proved. Birkhoff, G.: Hydrodynamics, Princeton, New Jersey, Princeton University Press, 1960. Cherkesov, L. V.: Hydrodynamics of waves, Kiev: "Naukova Dumka", 260 pp., 1980 (in Russian). Craik, A. D. D. and Leibovich, S.: A rational model for Langmuir circulations, J. Fluid Mech., 73, 4001–426, 1976. Gill, A. E.: Atmosphere-Ocean Dynamics, Academic Press, London Ltd., 1982. % Department of Applied % mathematics and Theoretical Physics University Cambridge Cambridge, % England. Kochin, N. E., Kibel, I. A., and Roze, N. V.: Theoretical Hydromechanics, Interscience Publishers, John Wiley & Sons, 1964. Kondrat'ev, K. Ya., Nikanorov, A. M., Pantuhin, Ya. V., and Zavolzhensky, M. V.: Ekman drift and other currents in unbounded regions, Doklady Akademii Nauk USSR, 310(5), 1070–1074, 1990. Lamb, H.: Hydrodynamics, Cambridge, The Univ. Press, 1932. Monin, A. S.: Hydrodynamics of atmosphere, ocean and Earth interior, St. Petersburg, Hydrometeoizdat, 524 pp., 1999. Nekrasov, A. I.: Exact theory of steady waves on the heavy fluid surface, Collection of works, V I. Phys. Math. Ed., 358–439, 1961. Sajjadi, S. G., Thomas, N. H., and Hunt, J. C. R.: Wind-over-Wave Couplings: Perspectives and Prospects, Oxford University Press, USA, 384 pp., 1999. Stocker, J. J.: Water Waves, Pure and Applied Mathematics, Vol 9, The Mathematical Theory and Applications, Institute of Mathematical Sciences, New York University, USA, 291–314, 1957. Struminskii, V. V.: On the theory of Boltzmann kinetic equation, RGD, Vol. 1, VI Int. Symp., N.Y., Akad. Press, 1969. Titov, L. F.: Wind waves, Hydro. Meteo. Ed., 294 pp., 1969 (in Russian). Zavolzhensky, M. V. and Rutkevich, P. B.: Large Reynolds Numbers: contour flows, Pr-2117 M., IKI RAS, 60 pp., 2006.