Turbulent dynamos beyond the heuristic modeling: Helicities and density variance

Abstract

Turbulence plays an essential role determining the transport of a system. Depending on the statistical properties of turbulence, properties of turbulent transport changes much. To understand the mechanisms that determine the dynamical balance of the enhancement and suppression of the turbulent transport, effects of several helicities are investigated in the framework of hydrodynamic (HD) and magnetohydrodynamic (MHD) turbulence. Non-uniform turbulent kinetic helicity density (correlation between the velocity and vorticity fluctuations) coupled with the mean absolute vorticity (antisymmetric part of the mean velocity shear) contributes to the suppression of the turbulent momentum transport represented by the eddy or turbulent viscosity in HD turbulence. Turbulent cross helicity (cross-correlation between the velocity and magnetic-field fluctuations) contributes to the suppression of the effective magnetic field transport represented by the turbulent magnetic diffusivity in MHD turbulence. In order to describe the turbulent transport, information of the intensity of fluctuations represented by the turbulent energies is not enough. Information of the structure of fluctuations represented by several helicities is also indispensable. In inhomogeneous turbulence, the transport coefficients expressed in terms of the energies and helicities are spatiotemporally inhomogeneous. For a self-consistent description of the turbulent flows in the real-world, the transport equations of turbulence quantities should be simultaneously solved with the counterparts of the mean fields.