Energy Transfer, Discontinuities, and Heating in the Inner Heliosphere Measured with a Weak and Local Formulation of the Politano-Pouquet Law

The solar wind is a highly turbulent plasma for which the mean rate of energy transfer ϵ 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 Dσ whose analytical form is derived from incompressible magnetohydrodynamics; it can be considered as a weak and local (in space) formulation of the PP98 law whose expression is recovered after integration in space. We used Dσ to estimate the local energy transfer rate at scale σ from the THEMIS-B and Parker Solar Probe 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 σ. We also observe that switchbacks seem to be characterized by a singular behavior with an energy transfer varying as σ -3/4, which slightly differs from classical discontinuities characterized by a σ -1 scaling. A comparison between the measurements of ϵ and Dσ shows that in general the latter is significantly larger than the former.