Yaglom law in the expanding solar wind

TL;DR

This paper extends the Yaglom law to the expanding solar wind context, revealing additional terms due to expansion that significantly impact turbulence energy cascade rate estimations.

Contribution

It introduces a modified Yaglom law incorporating solar wind expansion effects and demonstrates their importance using spacecraft data.

Findings

Expansion introduces two new terms in the Yaglom law.

New terms are comparable to the classical third order moment in the inertial range.

Neglecting these terms leads to inaccurate energy cascade rate estimates.

Abstract

We study the Yaglom law, which relates the mixed third order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two scales expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Els\"asser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom's third order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.