Abstract
Phenomenological theories of strong incompressible magnetohydrodynamic (MHD) turbulence derived by Goldreich and Sridhar (GS) in 1995 and by Boldyrev in 2006 are only applicable to turbulence with vanishing cross-helicity. In this study, these two theories are generalized to treat turbulence with nonvanishing cross-helicity in such a way that the relation (w+/w−)2=(e+/e−)2 observed in numerical simulations is satisfied. The average energy (second order structure function) in the generalized GS theory is E(r⊥)=ϕ1(σc)(er⊥)2/3 and that in the generalized Boldyrev theory is E(r⊥)=ϕ2(σc)(vAer⊥)1/2, where the function ϕ(σc) describes the dependence on the normalized cross-helicity σc. The form of the function ϕ(σc) is derived through a renormalization of the variable σc that yields a one parameter family of solutions. The theory derived by Lithwick, Goldreich, and Sridhar (LGS) in 2007 is a special case of the generalized GS theory derived here; however, other generalizations of the GS theory are obtained that ...
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