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The numerical simulation of wind-wave interaction

Published online by Cambridge University Press:  12 April 2006

D. V. Chalikov
D. V. Chalikov
Affiliation:
Leningrad Branch, P. P. Shirshov Institute of Oceanography, USSR Academy of Sciences, 30 Pervaya Liniya, Leningrad 199053, USSR
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Abstract

The Navier-Stokes equations for a two-layer flow are written in a curvilinear system of co-ordinates in which the height is measured from the interface. A technique for averaging the equations over an ensemble of wave surfaces which are not very different from each other is proposed. Moments which include deviations in the rate of surface displacement and in the slopes are dropped. It is assumed that the averaged equations describe the evolution of a large-scale velocity field. The moments of the turbulent velocity field are parameterized using the isotropic coefficient of turbulent viscosity, which, from dimensional considerations, is expressed in terms of the length scale growing linearly upwards and downwards from the interface and the turbulent kinetic energy. The equation defining the evolution of turbulent energy is derived without allowing for the curvilinearity of the system of co-ordinates. Laboratory experiments in a wind-water tunnel are simulated by integrating the equations numerically. The results are compared with measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 3 , 15 August 1978 , pp. 561 - 582
Copyright
© 1978 Cambridge University Press

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References

Barnett, T. P. & Kenyon, K. E. 1975 Recent advances in the study of wind waves. Rep. Prog. Phys. 38, 667–729.Google Scholar
Chalikov, D. V. 1976 A mathematical model of wind waves. Dokl. Akad. Nauk SSSR 197, 1083–1086.Google Scholar
Davis, R. E. 1970 On the turbulent flow over a wavy boundary. J. Fluid Mech. 42, 721–732.Google Scholar
Gent, P. R. 1977 A numerical model of the air flow above water waves. Part 2. J. Fluid Mech. 82, 349–369.Google Scholar
Gent, P. R. & Taylor, P. A. 1976 A numerical model of the air flow above waves. J. Fluid Mech. 77, 105–128.Google Scholar
Gent, P. R. & Taylor, P. A. 1977 A note on ‘separation’ over short wind waves. Boundary-Layer Met. 11, 65–87.Google Scholar
Kitaigorodsky, S. A. 1970 The Physics of Air–Sea Interaction. Leningrad: Gidrometeoizdat.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–204.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics. MIT Press.
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445.Google Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech. 4, 426–434.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Smagorinsky, J. 1974 Global atmospheric modelling and the numerical simulation of climate. In Weather and Climate Modification, pp. 633–686. Wiley.
Stewart, R. H. 1970 Laboratory studies of the velocity field over deep-water waves. J. Fluid Mech. 42, 733–754.Google Scholar
Taylor, P. A., Gent, P. R. & Keen, J. M. 1976 Some numerical solutions for turbulent boundary-layer flow above fixed, rough, wavy surfaces. Geophys. J. Roy. Astr. Soc. 44, 177–201.Google Scholar
Zilitinkevich, S. S. 1970 The Dynamics of the Atmospheric Boundary Layer. Leningrad: Gidrometeoizdat.