Residual Energy in Weak and Strong MHD Turbulence

摘要

Recent numerical and observational studies revealed that spectra of magnetic and velocity fluctuations in MHD turbulence have different scaling indexes. This intriguing feature has been recently explained in the case of weak MHD turbulence, that is, turbulence consisting of weakly interacting Alfvén waves. However, astrophysical turbulence is strong in majority of cases. In the present work, we propose a unifying picture that allows one to address weak and strong MHD turbulence on the same footing. We argue that magnetic and kinetic energies are different in both weak and strong MHD turbulence. Their difference, the so-called residual energy, is spontaneously generated by turbulence, it has the Fourier spectrum E_r(k) = E_v(k) - E_b(k) ∝ - f_w(k_∥/k_⊥)k_⊥~(-2) in weak turbulence, and E_r(k) ∝ - f_s(k_∥/k_⊥) k_⊥~(-3) in strong turbulence. Here f_(w,s)(x) are functions declining fast for x > C_(w,s) and not significantly varying for x < C_(w,s) with some constants C_(w,s), and k_∥ and k_⊥ the field-parallel and field-perpendicular wave vectors with respect to the applied strong uniform magnetic field.