The third-order law for increments in magnetohydrodynamic turbulence with constant shear

TL;DR

This paper generalizes the third-order law for structure functions in homogeneous incompressible MHD turbulence to include the effects of constant shear, revealing a modified relation crucial for understanding plasma turbulence.

Contribution

The authors extend the third-order law in MHD turbulence to account for constant shear, providing a new relation that differs from the classical proportionality.

Findings

Shear modifies the third-order structure function relation.

The new law accounts for non-proportional dependence on separation.

Implications for laboratory and space plasma turbulence are discussed.

Abstract

We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic (MHD) turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation [Politano and Pouquet, Phys. Rev. E, 57 21 (1998)] between third-order structure functions and the dissipation rate in steady inertial range turbulence, in which the shear plays a crucial role. In particular, the presence of shear leads to a third-order law which is not simply proportional to the relative separation. Possible implications for laboratory and space plasmas are discussed.