Pubs.GISS: Abstract of Canuto et al. 1999

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Canuto et al. 1999

Canuto, V.M., M.S. Dubovikov, and G. Yu, 1999: A dynamical model for turbulence. VIII. IR and UV Reynolds stress spectra for shear-driven flows. Phys. Fluids, 11, 665-677, doi:10.1063/1.869938.

The basic equations for the two-point Reynolds stresses derived in paper II are solve analytically in two regimes: the UV (ultraviolet) region corresponding to the inertial range and the IR (infrared) region corresponding to k→0. The analytic treatment is possible due to the existence of two smallness parameters: U_i,j(k²ν_t)^-1 in the UV region and kL in the IR region; U_i,j is the mean velocity gradient, ν_t(k) is the turbulent viscosity, and L is the integral length scale. For an arbitrary flowm the Reynolds stress spectrum in the UV region is given by Eqs. (53)-(59). In the IR region, and in the first-order approximation in kL, the spectra coincide with those of the rapid distortion theory. Since they are flow independent, we shall discuss a few representative cases. The resulting Reynolds stress spectra, which are shown to reproduce existing data, are the basis for the calculation of the one-point Reynolds stresses to be presented in paper IX. The model has no free parameters.