# Generation of Large-scale Vorticity

__Description__

We studied the effect of a mean velocity shear on a turbulence and on the effective force which is
determined by the divergence of the Reynolds stresses. We found a possibility for 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. 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. We determined spatial characteristics of the instability, such as the minimum size of the growing perturbations and
the size of perturbations with the maximum growth rate. This instability and the
dynamics of the mean vorticity are associated with Prandtl’s turbulent secondary flows.

__References__

- T. Elperin, I. Golubev, N. Kleeorin, I. Rogachevskii, Large-scale instability in a sheared nonhelical turbulence: Formation of vortical structures,
*Physical Review E*, **76**, 066310, 2007.

PDF: 515 KB

- T. Elperin, N. Kleeorin, and I. Rogachevskii, Generation of Large-scale
Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear.
*Physical
Review E*, **68**, 016311(1-8), 2003.

PDF: 144 KB

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Department of Mechanical Engineering