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A new spectral theory of turbulence and heat transfer in stably stratified flows

DOI: 10.1615/ICHMT.2006.TurbulHeatMassTransf.990
pages 483-486

Semion Sukoriansky
Perlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

B. Galperin
College of Marine Science, University of South Florida, St. Petersburg, Florida 33701, USA

V. Perov
Department of Research and Development, Swedish Meteorological and Hydrological Institute, SE-601 76 Norrkoping, Sweden


A new spectral theory of stably stratified turbulence has been developed based upon a quasi-Gaussian approximation and a self-consistent procedure of small-scale modes elimination. The theory gives effective anisotropic eddy diffusivity and viscosity; their anisotropization increases with the strength of stratification measured by Ri or 1/Fr. While the horizontal mixing and momentum transport increase, their vertical counterparts decrease. Horizontal and vertical turbulent Prandtl numbers are computed as functions of Ri or Fr. The vertical Prandtl number, Prt, increases with Ri and is proportional to Ri at large Ri, in agreement with experimental data. This behaviour of Prt reflects the effect of internal gravity waves which do not transport scalars such as the temperature but do transport momentum. The theory also yields analytical expressions for various 1D and 3D spectra including the Corrsin - Obukhov spectrum.

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