QUENCHING AND ANISOTROPY OF HYDROMAGNETIC TURBULENT TRANSPORT

Abstract

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields\nthrough mean-field effects like turbulent diffusion and the $\\alpha$ effect.\nFor stronger fields, these effects are usually suppressed or quenched, and\nadditional anisotropies are introduced. Using different variants of the\ntest-field method, we determine the quenching of the turbulent transport\ncoefficients for the forced Roberts flow, isotropically forced non-helical\nturbulence, and rotating thermal convection. We see significant quenching only\nwhen the mean magnetic field is larger than the equipartition value of the\nturbulence. Expressing the magnetic field in terms of the equipartition value\nof the {\\it quenched} flows, we obtain for the quenching exponents of the\nturbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced\nturbulence, and convection, respectively. However, when the magnetic field is\nexpressed in terms of the equipartition value of the unquenched flows these\nquenching exponents become about 4, 1.5, and 2.3, respectively. For the\n$\\alpha$ effect, the exponent is about 1.3 for the Roberts flow and 2 for\nconvection in the first case, but 4 and 3, respectively, in the second. In\nconvection, the quenching of turbulent pumping follows the same power law as\nturbulent diffusion, while for the coefficient describing the $\\bf \\Omega\n\\times \\bf J$ effect nearly the same quenching exponent is obtained as for\n$\\alpha$. For forced turbulence, turbulent diffusion proportional to the second\nderivative along the mean magnetic field is quenched much less, especially for\nlarger values of the magnetic Reynolds number. However, we find that in\ncorresponding axisymmetric mean-field dynamos with dominant toroidal field the\nquenched diffusion coefficients are the same for the poloidal and toroidal\nfield constituents.\n