THE ROLE OF ANGULAR-MOMENTUM IN THE MAGNETIC DAMPING OF TURBULENCE

Landau & Lifshitz showed that Kolmogorov's E similar to t(-10/7) law f or the decay of isotropic turbulence rests on just two physical ideas: (a) the conservation of angular momentum, as expressed by Loitsyansky 's integral; and (b) the removal of energy from the large scales via t he energy cascade. Both Kolmogorov's original analysis and Landau & Li fshitz's reinterpretation in terms of angular momentum are now known t o be flawed. The existence of long-range velocity correlations means t hat Loitsyansky's integral is not an exact representation of angular m omentum, nor is it strictly conserved. However, in practice the long-r ange velocity correlations are weak and Loitsyansky's integral is almo st constant, so that the Kolmogorov/Landau model provides a surprising ly simple and robust description of the decay. In this paper we redeve lop these ideas in the context of MHD turbulence. We take advantage of the fact that the angular momentum of a fluid moving in a uniform mag netic field has particularly simple properties. Specifically, the comp onent parallel to the magnetic field is conserved while the normal com ponents decay exponentially on a time scale of tau = rho/sigma B-2 We show that the counterpart of Loitsyansky's integral for MHD turbulence is integral x(perpendicular to)(2)Q(perpendicular to)dx, where Q(ij) is the velocity correlation. When the long-range correlations are weak this integral is conserved. This provides an estimate of the rate of decay of energy. At low values of magnetic field we recover Kolmogorov 's law. At high values we find E similar to t(-1/2), which is a result derived earlier by Moffatt. We also show that integral x(perpendicula r to)(2) Q(parallel to)dx decays exponentially on a time scale of tau. We interpret these results in terms of the behaviour of isolated vort ices orientated normal and parallel to the magnetic field.