von K\'arm\'an-Howarth equation for three-dimensional two-fluid plasmas

TL;DR

This paper derives an exact turbulence law for three-dimensional two-fluid plasmas, extending classical fluid dynamics results to plasma physics and providing a tool for analyzing solar wind turbulence.

Contribution

It introduces the von Kármán-Howarth equation for two-fluid plasmas and derives an analog of the four-fifth law, linking correlation functions to turbulent energy transfer.

Findings

Derivation of the von Kármán-Howarth equation for two-fluid plasmas

An exact four-fifth law for plasma turbulence in the large Reynolds number limit

A practical expression for in-situ solar wind measurements

Abstract

We derive the von K\'arm\'an-Howarth equation for a full three dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifth" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in-situ measurements in the solar wind at different spatial ranges.