MHD Inertial and Energy-containing Range Turbulence Anisotropy in the Young Solar Wind

We study solar wind turbulence anisotropy in the inertial and energy-containing ranges in the inbound and outbound directions during encounters 1-9 by the Parker Solar Probe (PSP) for distances between similar to 21 and 65 R circle dot. Using the Adhikari et al. approach, we derive theoretical equations to calculate the ratio between the 2D and slab fluctuating magnetic energy, fluctuating kinetic energy, and the outward/inward Elsasser energy in the inertial range. For this, in the energy-containing range, we assume a wavenumber k -1 power law. In the inertial range, for the magnetic field fluctuations and the outward/inward Elsasser energy, we consider that (i) both 2D and slab fluctuations follow a power law of k -5/3, and (ii) the 2D and slab fluctuations follow the power laws with k -5/3 and k -3/2, respectively. For the velocity fluctuations, we assume that both the 2D and slab components follow a k -3/2 power law. We compare the theoretical results of the variance anisotropy in the inertial range with the derived observational values measured by PSP, and find that the energy density of 2D fluctuations is larger than that of the slab fluctuations. The theoretical variance anisotropy in the inertial range relating to the k -5/3 and k -3/2 power laws between 2D and slab turbulence exhibits a smaller value in comparison to assuming the same power law k -5/3 between 2D and slab turbulence. Finally, the observed turbulence energy measured by PSP in the energy-containing range is found to be similar to the theoretical result of a nearly incompressible/slab turbulence description.