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 η and kinematic viscosity ν is considered. It is proved then that if v×B and (∇×v)×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=B₀ exp(-α²ηt)b, v=v₀ exp(-α²νt)b, where b=b(r) such that ∇×b=αb, ∇ṡb=0 and B₀, v₀, and α are constants. Purely hydrodynamic flows are a particular case with B₀=0. A simple example of a chaotic force-free field is also constructed.