Dynamic Phase Alignment in Inertial Alfvén Turbulence

In weakly collisional plasma environments with sufficiently low electron beta, Alfv\'enic turbulence transforms into inertial Alfv\'enic turbulence at scales below the electron skin depth, k_⊥dₑ1. We argue that, in inertial Alfv\'enic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as cosαₖ∝k_⊥^-1. The kinetic and magnetic energy spectra scale as ∝k_⊥^-5/3 and ∝k_⊥^-11/3, respectively. As a result of the dual direct cascade, the generalized helicity spectrum scales as ∝k_⊥^-5/3, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the k_⊥dₑ1 range. Turbulent eddies exhibit a phase-space anisotropy k_∥∝k_⊥5/3, consistent with critically balanced inertial Alfv\'en fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, and nonrelativistic pair plasmas, as well as to strongly rotating nonionized fluids.