Universal turbulent relaxation of fluids and plasmas by the principle of vanishing nonlinear transfers

TL;DR

This paper introduces a new principle of vanishing nonlinear transfer to unify the turbulent relaxation process in fluids and plasmas, providing a clear method to determine relaxed states without variational approaches.

Contribution

It proposes a novel principle that unifies turbulent relaxation theories for fluids and plasmas, enabling unambiguous determination of relaxed states.

Findings

Relaxed states support a pressure gradient consistent with numerical studies.

Relaxed states reduce to Beltrami-type aligned states with negligible pressure gradient.

The new principle simplifies the understanding of turbulent relaxation processes.

Abstract

A seventy year old problem of fluid and plasma relaxation has been revisited. A new principle of vanishing nonlinear transfer has been proposed to develop a unified theory of turbulent relaxation of neutral fluids and plasmas. Unlike previous studies, the new principle enables us to find the relaxed states unambiguously without going through any variational principle. The general relaxed states obtained herein are found to support naturally a pressure gradient which is consistent with several numerical studies. Relaxed states are reduced to Beltrami type aligned states where the pressure gradient is negligibly small.