D-dimensional developed MHD turbulence: double expansion model

Abstract

Abstract. Developed magnetohydrodynamic turbulence near two dimensions d up to three dimensions has been investigated by means of renormalization group approach and double expansion regularization. A modification of standard minimal subtraction scheme has been used to analyze the stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. The exact analytical expressions have been obtained for the fixed points. The continuation of the universal value of the inverse Prandtl number u = 1.562 determined at d = 2 up to d = 3 restores the value of u = 1.393 which is known in the kinetic fixed point from usual ǫ-expansion. The magnetic stable fixed point has been calculated and its stability region has been also examined. This point losses stability: (1) below critical value of dimension dc = 2.36 (independently on the a-parameter of a magnetic forcing) and, (2) below the value of ac = 0.146 (independently on the dimension).

The spontaneous magnetic field direction in an anisotropic MHD dynamo

“…The com plete unrenormalized ac tion of the anisotropically forced MHD tur bu lence [18,19] with the shifted MF (b b C ® + ) [3] can be ob tained using f and f in the sto chas tic MHD equa tions (1). Us ing the standart for malism, the sto chas tic prob lem (1) with correlator (4) can be trans formed into the field the o ret i cal model of fields F = {v, b, v¢, b¢} where v¢, b¢ are the auxil iary in com press ible fields with the ac tion (see [1,36], for de tails):…”

Long-range Interactions, Stochasticity and Fractional Dynamics

“…Fully developed magneto-hydrodynamic turbulence near d = 2 up to d = 3 has been investigated in (Jurcisin and Stehlik, 2006) by means of renormalization group approach and double expansion regularization. A modification of standard minimal subtraction scheme has been used to analyze the stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point.…”