Residual Energy in Weak and Strong MHD Turbulence
  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 Alfven 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) \propto
-f_w(k_||/k_perp) k_perp^{-2} in weak turbulence, and E_r(k) \propto
-f_s(k_||/k_perp) k_perp^{-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_perp the field-parallel and
field-perpendicular wave vectors with respect to the applied strong uniform
magnetic field.
