On the nature of chaotic regions in dissipative hydrodynamics and magnetohydrodynamics

A region with chaotic magnetic field lines where the magnetic field (B) and plasma velocity (v) are continuous and differentiable and satisfy the dissipative incompressible magnetohydrodynamic equations with magnetic diffusivity eta and kinematic viscosity nu is considered. It is proved then that if v x B and (del x v) x v are potential, the structurally stable solutions describing such chaotic regions are characterized by a decaying linear magnetic force-free field and Beltrami flow of the form B=B-0 exp(-alpha(2) eta t) b, v=v(0) exp(-alpha(2) nu t) b, where b=b(r) such that del x b = alpha b, del . b=0 and B-0, nu(0), and alpha are constants. Purely hydrodynamic flows are a particular case with B-0=0. A simple example of a chaotic force-free field is also constructed. (C) 1999 American Institute of Physics. [S1070-664X(99)03804-5].