Energy transfer, discontinuities and heating in the inner solar wind measured with a weak and local formulation of the Politano-Pouquet law

TL;DR

This paper introduces a new local method to measure energy transfer in the solar wind, revealing the impact of discontinuities and switchbacks on energy dissipation at various scales.

Contribution

A novel weak and local formulation of the Politano-Pouquet law is developed, enabling analysis of energy transfer in the presence of discontinuities in the solar wind.

Findings

Discontinuities near the Sun cause strong energy transfer across scales.

Switchbacks exhibit a unique $\sigma^{-3/4}$ scaling in energy transfer.

The local energy transfer rate $ ext{ extlbrackdbl} ext{ extperthousand} ext{ extbrackdbl}$ is generally larger than the mean rate $ ext{ extlbrackdbl} ext{ extperthousand} ext{ extbrackdbl}$.

Abstract

The solar wind is a highly turbulent plasma for which the mean rate of energy transfer $\varepsilon$ has been measured for a long time using the Politano-Pouquet (PP98) exact law. However, this law assumes statistical homogeneity that can be violated by the presence of discontinuities. Here, we introduce a new method based on the inertial dissipation $\Dis$ whose analytical form is derived from incompressible magnetohydrodynamics (MHD); it can be considered as a weak and {\it local} (in space) formulation of the PP98 law whose expression is recovered after integration is space. We used $\Dis$ to estimate the local energy transfer rate from the \textit{THEMIS-B} and \textit{Parker Solar Probe} (PSP) data taken in the solar wind at different heliospheric distances. Our study reveals that discontinuities near the Sun lead to a strong energy transfer that affects a wide range of scales $\sigma$. We also observe that switchbacks seem to be characterized by a singular behavior with an energy transfer varying as $\sigma^{-3/4}$, which slightly differs from classical discontinuities characterized by a $\sigma^{-1}$ scaling. A comparison between the measurements of $\varepsilon$ and $\Dis$ shows that in general the latter is significantly larger than the former.