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

Abstract

Abstract The 2D + slab superposition model of solar wind turbulence has its theoretical foundations in nearly incompressible magnetohydrodynamics (NI MHD) in the plasma beta ∼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 Elsässer variables in the 2D + NI/slab model. We find that (1) the majority 2D component has a power spectrum in perpendicular wavenumber k ⊥; (2) the strongly imbalanced minority NI/slab turbulence has power spectra and , where k z 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) ∼ k −5/3 and corresponding to strong turbulence and the flatter spectrum satisfying G*(k) ∼ k −3/2 and corresponding to weak turbulence; (4) there is a critical balance regime for NI/slab turbulence that satisfies and ; and (5) the forward and backward Elsässer power spectra can have different spectral forms provided that the triple-correlation 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 Alfvén timescales are both finite.