Dynamic Phase Alignment in Navier-Stokes Turbulence.

In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling ∝k^{-5/3}. We demonstrate via direct numerical simulations that the two cascades are compatible due to the existence of a strong scale-dependent phase alignment between velocity and vorticity fluctuations, with the phase alignment angle scaling as cosα_{k}∝k^{-1}.

Dynamic Phase Alignment in Inertial Alfvén Turbulence.

In weakly collisional plasma environments with sufficiently low electron beta, Alfvénic turbulence transforms into inertial Alfvénic turbulence at scales below the electron skin depth, k_{⊥}d_{e}≳1. We argue that, in inertial Alfvénic 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 cosα_{k}∝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_{⊥}d_{e}≫1 range. Turbulent eddies exhibit a phase-space anisotropy k_{∥}∝k_{⊥}^{5/3}, consistent with critically balanced inertial Alfvén 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.