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In a previous work (MGV18), we showed numerically that the turbulent cascadegenerated by quasi-2D structures (with wave vectors mostly-perpendicular to themean magnetic field) is able to generate a temperature profile close to the oneobserved in solar wind ($\simeq 1/R$) in the range 0.2 $\le R \le$ 1 au.Theory, observations and numerical simulations point to another robuststructure, the radial-slab, with dominant wave vectors along the radial: westudy here the efficiency of the radial-slab cascade in building the $1/R$temperature profile. As in MGV18, we solve the three-dimensional MHD equationsincluding expansion to simulate the turbulent evolution. We find that anisotropic 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 rateclose to $1/R$ but with a radial-slab anisotropy at 1 au. Surprisingly, theturbulent cascade concentrates in the plane transverse to the radial direction,displaying 1D spectra with scalings close to $k^{-5/3}$ in this plane. Thissupports both the idea of turbulent heating of the solar wind, and theexistence of two different turbulent cascades, quasi-2D and radial slab, at theorigin of the heating.  We conclude that sampling the radial spectrum in the solar wind may give buta poor information on the real cascade regime and rate when the radial slab isa non-negligible part of turbulence.

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