Relaxed States of Alfvenic Turbulence

By applying the Taylor's relaxation hypothesis, we investigate the relaxed states of the Alfvenic turbulence which is represented here through the Derivative Nonlinear Schroedinger Equation (DNLS). We choose the three lowest order invariants of the DNLS and demonstrate their differential dissipation. We also demonstrate the process of inverse cascade of energy through the mode-mode interaction in the DNLS with dissipation. We perform two variational problems. The variational equation derived using the two lowest-order invariants describes a `constant b', force--free state. However the relaxed state derived using the three lowest order invariants turns out to be equivalent to the steady state of the DNLS. Thus we conclude that the Alfvenic turbulence relaxes or self--organises to a state with soliton type structures which, under certain conditions, approaches the `constant b' force--free state. We believe that the solar wind may be one of physical sites of Alfvenic turbulence to have the right circumstances for the verification of some of these results.