On the suppression of turbulence by a uniform magnetic field

Abstract

The suppression of initially isotropic turbulence by the sudden application of a uniform magnetic field is considered. The problem is characterized by three dimensionless numbers, a Reynolds number R, a magnetic Reynolds number Rm and a magnetic interaction parameter N (for definitions, see equations (1.2) and (1.4)). It is supposed that R [Gt ] 1, Rm [Lt ] 1 and N [Gt ] 1. There are two important time scales, ta a time characteristic of magnetic suppression, and t0 = Ntd, the ‘turn-over’ time of the turbulent energy-containing eddies. For 0 < t [Lt ] t0 the response of the energy-containing components of the turbulence to the applied field is linear and the time dependence of the kinetic energy density K(t) and magnetic energy density M(t) are analysed. There are essentially two distinct contributions to each from two domains of wave-number space D1 and D2 (defined in figure 2). In D1 the response is severely anisotropic, while in D2 it is nearly isotropic. The relative importance of the contributions K1(t) (from D1) and K2(t) (from D2) to K(t) depends on the value of the Lundquist number S = (NRm)½. If S [Lt ] 1, then K1(t) dominates for all t [lsim ] t0 and K(t) ∝ t−½ for td [Lt ] t [Lt ] t0. If 1 [Lt ] S [Lt ] R−2m, then a changeover in the dominant contribution occurs when t = O(S½Rm) t0. Analogous results are obtained for the magnetic energy density.