von Kármán-Howarth relationship for helical magnetohydrodynamic flows

Area of Science:

• Physics
• Astrophysics
• Fluid Dynamics

Background:

• Homogeneous isotropic magnetohydrodynamic (MHD) turbulent flows are crucial in astrophysics.
• Existing formulations like the von Kármán-Howarth (VKH-HM) equation describe kinetic energy but not helical flows.
• Helical MHD is relevant to phenomena in the solar corona, interstellar medium, and dynamo theory.

Purpose of the Study:

• To derive an exact equation for homogeneous isotropic magnetohydrodynamic (MHD) turbulent flows with nonzero helicity.
• To extend the classical von Kármán-Howarth (VKH-HM) formulation to helical MHD.
• To analyze the implications for astrophysical flows and dynamo problems.

Main Methods:

• Derivation of an exact equation using a new tensor formulation for helical MHD.
• Analysis of third-order tensors, requiring four generating functions due to nonmirror invariance.
• Investigation of the relationship between magnetic helicity dissipation and third-order correlations.

Main Results:

• An exact equation, termed VKH-HM, for helical MHD turbulent flows was derived.
• Four generating functions are necessary for helical fluids, unlike the two for isotropic fluids.
• The equation links magnetic helicity dissipation to correlations of velocity, magnetic field, and magnetic potential.

Conclusions:

• The derived VKH-HM equation provides a new framework for studying helical MHD turbulence.
• In the long-time, nonresistive limit, a linear scaling of a third-order tensor is observed.
• This scaling correlates components of the electromotive force and magnetic potential, offering insights into astrophysical dynamics.