Generation of large-scale vorticity in rotating stratified turbulence with inhomogeneous helicity: mean-field theory

Abstract

We discuss a mean-field theory of the generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale non-uniform flow is produced due to either a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known as a vorticity dynamo) due to a combined effect of the large-scale shear and Reynolds stress-induced generation of the mean vorticity. The latter is due to the effect of large-scale shear on the Reynolds stress. A fast rotation suppresses this large-scale instability.

Compressibility in turbulent magnetohydrodynamics and passive scalar transport: mean-field theory

“…We also do not consider here effects related to the non-uniformity of kinetic helicity ( ) or the combined effect of stratification and kinetic helicity ( ), because their contributions to the mean electromotive force are much smaller in comparison with the standard contributions to the mean electromotive force caused by the turbulent motions (they are of the order of the terms we neglected in the present study). The non-uniformity of kinetic helicity (Yokoi & Yoshizawa 1993; Yokoi & Brandenburg 2016; Kleeorin & Rogachevskii 2018) or the combined effect of stratification and kinetic helicity (Kleeorin & Rogachevskii 2018) contribute to the generation of large-scale vorticity or large-scale shear motions.…”

“…Different contributions to (2.12) have been discussed by Batchelor (1953), Elperin, Kleeorin & Rogachevskii (1995), Rädler, Kleeorin & Rogachevskii (2003), Rogachevskii & Kleeorin (2018) and Kleeorin & Rogachevskii (2018). Note that for a purely potential flow, equation (2.12) for the background turbulence is used in the limit , which yields …”

Vortex Dynamo in Rotating Media

“…This theory was confirmed in a number of numerical and analytical calculations [20]. Large-scale vortex instability in rotating turbulent flows has been studied in many papers [21]- [24]. So, when considering rotating convective systems, attempts were made to apply the results obtained to the theory of the occurrence of tropical cyclones.…”

“…So, when considering rotating convective systems, attempts were made to apply the results obtained to the theory of the occurrence of tropical cyclones. The linear theory of the vortex dynamo [15]- [24] is best developed within the framework of the statistical approach, which also uses the second-order correlation approximation. Thus, the question arose about the mechanisms of saturation of large-scale instability and the emergence of stationary vortex structures.…”

Transport in helical fluid turbulence

“…In the following, we treat the vortex dynamo problem from the viewpoint of the inhomogeneous helicity effect [Yokoi & Yoshizawa, 1993, Yokoi & Brandenburg, 2016, Kleeorin & Rogachevskii, 2018.…”