Relaxed States of MHD Turbulence: Minimum Dissipation or Minimum Energy?

Abstract

Driven, dissipative MHD fluids often seem to undergo relaxation processes. After a turbulent formation phase, a geometrically simpler and less disordered configuration emerges. The best known example is the laboratory reversed-field pinch (RFP); similar field topologies have been proposed for solar prominences and astrophysical “flux ropes.” In a transient situation, the more rapid decay of kinetic and magnetic energy relative to magnetic helicity provides a mechanism for generating an MHD configuration with several similarities to observed RFP states. (This is the Taylor hypothesis, not unrelated to turbulent inverse magnetic cascades.) For the driven steady state, however, all quantities are supplied at the same time-averaged rate at which they are dissipated, by definition; nothing decays relative to anything else. Some other unifying principle, beyond “minimum energy” or “selective decay,” seems necessary to describe the results of driven, steady-state MHD computations. We have been attempting to adapt the principle of minimum energy dissipation rate to MHD. It is a 19th century principle that achieved some success in hydrodynamics and separately in dissipative electrodynamics.