Consistency of von Karman Decay Rate with the Energy Supply Rate and Heating Rate Observed by Parker Solar Probe

The von Kármán-Howarth equations give a starting basis for the classical turbulence theory. The formula for the magnetohydrodynamics von Kármán decay rate represents an energy source in many solar wind models with turbulence as the driver. However, it still lacks the radial trend comparison between the von Kármán decay rate, the energy supply rate, and the perpendicular heating rate based on direct observations of the solar wind. Here we carry out this kind of comparison for the first time using Parker Solar Probe measurements from its first three orbits. We find that the radial variation of the von Kármán decay rate is consistent with that of both the energy supply rate and the heating rate in the slow solar wind. These results support the idea that the von Kármán decay law is an active process responsible for solar wind heating. These results also suggest a new idea that both the von Kármán decay law and the low-frequency break sweeping may be controlled by the same nonlinear process. Some limitations of the present study are also addressed.