Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear

An effect of a mean velocity shear on a turbulence and on the effective force which is determined by the gradient of Reynolds stresses is studied. Generation of a mean vorticity in a homogeneous incompressible turbulent flow with an imposed mean velocity shear due to an excitation of a large-scale instability is found. The instability is caused by a combined effect of the large-scale shear motions (''skew-induced" deflection of equilibrium mean vorticity) and ''Reynolds stress-induced" generation of perturbations of mean vorticity. Spatial characteristics, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This instability and the dynamics of the mean vorticity are associated with the Prandtl's turbulent secondary flows. This instability is similar to the mean-field magnetic dynamo instability. Astrophysical applications of the obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.

Formation of Large-Scale Semi-Organized Structures in Turbulent Convection

A new mean-field theory of turbulent convection is developed. This theory predicts the convective wind instability in a shear-free turbulent convection which causes formation of large-scale semi-organized fluid motions in the form of cells or rolls. Spatial characteristics of these motions, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This study predicts also the existence of the convective shear instability in a sheared turbulent convection which results in generation of convective shear waves with a nonzero hydrodynamic helicity. Increase of shear promotes excitation of the convective shear instability. Applications of the obtained results to the atmospheric turbulent convection and the laboratory experiments on turbulent convection are discussed. This theory can be applied also for the describing a mesogranular turbulent convection in astrophysics.Comment: 16 pages, 10 figures, REVTEX4, PHYSICAL REVIEW E, v. 67, in press (2003