Universal relations between parallel and perpendicular spectral power-law exponents in nonaxisymmetric magnetohydrodynamic turbulence

Following a general heuristic approach, algebraic constraints are established between the parallel and perpendicular power-law exponents of nonaxisymmetric, highly aligned magnetohydrodynamic turbulence, both with and without a strong imbalance between the Elsässer variables. Such relations are universal for both regimes of weak and strong turbulence and are useful to predict the corresponding turbulent power spectra. For a scale-dependent alignment, a Boldyrev-type -3/2 perpendicular spectrum emerges transverse to the direction of alignment, whereas a -5/3 spectrum is obtained for the same if the alignment becomes scale-independent. However, regardless of the nature of alignment, our analysis consistently yields a k_{∥}^{-2} spectrum commonly observed in both numerical simulations and in situ data of solar wind. In the appropriate limit, previously obtained algebraic relations and power spectra for axisymmetric MHD turbulence (Galtier, Pouquet, and Mangeney, Physics of Plasmas, 2005) are successfully recovered. Finally, more realistic relations capturing weak Alfvén turbulence (with constant k_{∥}) and the transition to strong turbulence are derived along with their corresponding power spectra.