Turbulence in Magnetohydrodynamics

Abstract

The most interesting and probably the least understood flow problem is the turbulent flow. The essential characteristic of turbulent flow is that the turbulent fluctuations are random in nature; hence, the final and logical solution of the turbulence problem requires the application of the methods of statistical mechanics. Considerable progress has been made in this respect during the last twenty years but there are still many important problems to be solved before a successful statistical theory of turbulence can be developed (7). At the present time, most of the results from the statistical theory of turbulence are concerned with isotropic turbulence which was first investigated by G. I. Taylor and which was further developed by Yon Kármán, Kolmogoroff, Afisenberg and others. In magnetohydrodynamics, the problem is much more complicated, because we have to consider both the turbulent fluctuations in the magnetic field as well as those in the velocity field and their interaction. It was Chandrasekhar who extended the ordinary statistical theory of isotropic turbulence to the case of magnetohydrodynamics (2). He was able to show that many well-known results of the invariant theory of isotropic turbulence can be extended in magnetohydrodynamics. We are going to discuss Chandrasekhar’s statistical theory of isotropic turbulence in this chapter (§§ 2 to 6, and 8).