Comparing Turbulent Cascades and Heating versus 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 wavevectors mostly perpendicular to the mean magnetic field) is able to generate a temperature profile close to the one observed in solar wind (≃1/R) in the range 0.2 ≤ R ≤ 1 au. Theory, observations, and numerical simulations point to another robust structure, the radial slab, with dominant wavevectors 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 magnetohydrodynamic equations including expansion to simulate the turbulent evolution. We find that an isotropic distribution of wavevectors 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, associated to quasi-2D and radial-slab geometries. We conclude that sampling the radial spectrum in the solar wind may give poor information on the real cascade regime and rate when the radial slab is a non-negligible part of turbulence.