Abstract
The effects of self-amplification of a vorticity field in 3D turbulence and a vorticity gradient in 2D turbulence are considered. The conditionally averaged tensor of strain rates (with fixed vorticity) is obtained for 3D turbulence. The corresponding tensor (with fixed vorticity gradient) is obtained for 2D turbulence. These results are discussed in the context of observations and direct numerical simulations of turbulent flows. In particular, the appearance of 'vortex strings' in 3D turbulent flows is in accord with the obtained formula. The presented method is quite general and can be applied to a variety of physical systems with strong interaction.
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