Dynamic Phase Alignment in Inertial Alfven Turbulence

In weakly-collisional plasma environments with sufficiently low electron beta, Alfvenic turbulence transforms into inertial Alfvenic turbulence at scales below the electron skin-depth. We argue that, in inertial Alfvenic 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 proportional to the perpendicular wavenumber to the power of -1. The kinetic and magnetic energy spectra scale as the perpendicular wavenumber to the power of -5/3 and -11/3, respectively. As a result of the dual direct cascade, the generalized-helicity spectrum scales as the perpendicular wavenumber to the power of -5/3, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the sub-electron-skin-depth range. Turbulent eddies exhibit a phase-space anisotropy, with the parallel wavenumber scaling as the perpendicular wavenumber to the power of 5/3, consistent with critically-balanced inertial Alfven fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, non-relativistic pair plasmas, as well as to strongly rotating non-ionized fluids.

在电子β（electron beta）足够低的弱碰撞等离子体环境中，当尺度小于电子趋肤深度（electron skin-depth）时，阿尔文湍流（Alfvenic turbulence）会转变为惯性阿尔文湍流（inertial Alfvenic turbulence）。我们提出，在惯性阿尔文湍流中，能量与广义动力学螺旋度均呈现直接级联（direct cascades）特性。我们证明，由于速度与磁场涨落间的相位对准角存在显著的尺度依赖性，且该相位对准角的标度律正比于垂直波数的-1次幂，因此这两种级联是自洽兼容的。动力学能量谱与磁能谱的标度律分别正比于垂直波数的-5/3次幂与-11/3次幂。得益于这一双重直接级联过程，广义螺旋度谱的标度律正比于垂直波数的-5/3次幂，这意味着在亚电子趋肤深度范围内，随着级联向更小尺度推进，湍流将逐渐趋于平衡。湍流涡旋呈现出相空间各向异性，其平行波数的标度律正比于垂直波数的5/3次幂，这与临界平衡的惯性阿尔文涨落（inertial Alfven fluctuations）相符。我们的研究结果可应用于多种地球物理、空间与天体物理环境，包括地球磁鞘（magnetosheath）与电离层（ionosphere）、日冕（solar corona）、非相对论性正负电子等离子体，以及强旋转非电离流体。