On the suppression of turbulence by a uniform magnetic field

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 t 0 = Nt d , the ‘turn-over’ time of the turbulent energy-containing eddies. For 0 < t Lt t 0 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 D 1 and D 2 (defined in figure 2). In D 1 the response is severely anisotropic, while in D 2 it is nearly isotropic. The relative importance of the contributions K 1 ( t ) (from D 1 ) and K 2 ( t ) (from D 2 ) to K ( t ) depends on the value of the Lundquist number S = ( NR m ) ½ . If S Lt 1, then K 1 ( t ) dominates for all t lsim t 0 and K ( t ) ∝ t −½ for t d Lt t Lt t 0 . If 1 Lt S Lt R −2 m , then a changeover in the dominant contribution occurs when t = O ( S ½ R m ) t 0 . Analogous results are obtained for the magnetic energy density.