Spectral Anisotropy in 2D plus Slab Magnetohydrodynamic Turbulence in the Solar Wind and Upper Corona

The 2D + slab superposition model of solar wind turbulence has its theoretical foundations in nearly incompressible magnetohydrodynamics (NI MHD) in the plasma beta similar to 1 or << 1 regimes. Solar wind turbulence measurements show that turbulence in the inertial range is anisotropic, for which the superposition model offers a plausible explanation. We provide a detailed theoretical analysis of the spectral characteristics of the Elsasser variables in the 2D + NI/slab model. We find that (1) the majority 2D component has a power spectrum G(infinity)(k(perpendicular to)) similar to k(perpendicular to)(-5/3) in perpendicular wavenumber k(perpendicular to); (2) the strongly imbalanced minority NI/slab turbulence has power spectra G*(k(perpendicular to)) similar to k(-5/3) and G*(k(z)) similar to k(z)(-5/3), where kz is aligned with the mean magnetic field; (3) NI/slab turbulence can exhibit a double-power-law spectrum, with the steeper part being G*(k) similar to k(-5/3) and corresponding to strong turbulence and the flatter spectrum satisfying G*(k) similar to k(-3/2) and corresponding to weak turbulence; (4) there is a critical balance regime for NI/slab turbulence that satisfies G*(k(z)) similar to k(z)(-2) and G*(k(perpendicular to)) similar to k(-5/3); and (5) the forward and backward Elsasser power spectra can have different spectral forms provided that the triplecorrelation times for each are different. We use the spectral analysis to compute the total power spectra in frequency parallel to the solar wind flow for the superposition model, showing that strongly imbalanced turbulence yields an f(-5/3) spectrum for all angles between the mean flow and magnetic field, and that double power laws are possible when the nonlinear and Alfven timescales are both finite.