Comparing turbulent cascades and heating vs spectral anisotropy in solar wind via direct simulations

In a previous work (MGV18), we showed numerically that the turbulent cascade generated by quasi-2D structures (with wave vectors mostly-perpendicular to the mean magnetic field) is able to generate a temperature profile close to the one observed in solar wind ($\simeq 1/R$) in the range 0.2 $\le R \le$ 1 au. Theory, observations and numerical simulations point to another robust structure, the radial-slab, with dominant wave vectors along the radial: we study here the efficiency of the radial-slab cascade in building the $1/R$ temperature profile. As in MGV18, we solve the three-dimensional MHD equations including expansion to simulate the turbulent evolution. We find that an isotropic distribution of wave vectors with large cross helicity at 0.2 au, along with a large wind expansion rate, lead again to a temperature decay rate close to $1/R$ but with a radial-slab anisotropy at 1 au. Surprisingly, the turbulent cascade concentrates in the plane transverse to the radial direction, displaying 1D spectra with scalings close to $k^{-5/3}$ in this plane. This supports both the idea of turbulent heating of the solar wind, and the existence of two different turbulent cascades, quasi-2D and radial slab, at the origin of the heating. We conclude that sampling the radial spectrum in the solar wind may give but a poor information on the real cascade regime and rate when the radial slab is a non-negligible part of turbulence.