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 R_m and a magnetic interaction parameter N (for definitions, see equations (1.2) and (1.4)). It is supposed that R [Gt ] 1, R_m [Lt ] 1 and N [Gt ] 1. There are two important time scales, t_a a time characteristic of magnetic suppression, and t₀ = Nt_d, 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 = (NR_m)^½. If S [Lt ] 1, then K₁(t) dominates for all t [lsim ] t₀ and K(t) ∝ t^−½ for t_d [Lt ] t [Lt ] t₀. If 1 [Lt ] S [Lt ] R⁻²_m, then a changeover in the dominant contribution occurs when t = O(S^½R_m) t₀. Analogous results are obtained for the magnetic energy density.