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 the Reynolds stresses is studied. Generation of a mean vorticity in a homogeneous incompressible nonhelical 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 of the instability, 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 Prandtl's turbulent secondary flows.