RESUMEN
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 âk^{-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}âk^{-1}.
RESUMEN
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_{â¥}d_{e}â³1. 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}âk_{â¥}^{-1}. The kinetic and magnetic energy spectra scale as âk_{â¥}^{-5/3} and âk_{â¥}^{-11/3}, respectively. As a result of the dual direct cascade, the generalized helicity spectrum scales as âk_{â¥}^{-5/3}, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the k_{â¥}d_{e}â«1 range. Turbulent eddies exhibit a phase-space anisotropy k_{â¥}âk_{â¥}^{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.