Higher-order Analysis of Three-dimensional Anisotropy in Imbalanced Alfvénic Turbulence

Abstract We examine the applicability of homogeneous, negligible cross-helicity magnetohydrodynamic (MHD) turbulence models incorporating “critical balance” (CB) and “scale-dependent dynamic alignment” (SDDA) to Parker Solar Probe observations of a highly Alfvénic, high cross-helicity solar wind stream. At energy-injection scales, both Alfvénic modes satisfy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>χ</mml:mi> <mml:mi>λ</mml:mi> <mml:mo>±</mml:mo> </mml:msubsup> <mml:mo>≡</mml:mo> <mml:msubsup> <mml:mi>τ</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> <mml:mo>±</mml:mo> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>τ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> <mml:mo>±</mml:mo> </mml:msubsup> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>τ</mml:mi> <mml:mi mathvariant="normal">A</mml:mi> <mml:mo>±</mml:mo> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>τ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> </mml:mrow> <mml:mo>±</mml:mo> </mml:msubsup> </mml:math> denote the linear and nonlinear timescales. The outward cascade remains weak, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>≈</mml:mo> <mml:mn>0.2</mml:mn> </mml:math> , across all scales, while the inward cascade reaches CB at the onset of the inertial range ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> </mml:math> ), yet with spectral scalings that depart from the canonical weak-to-strong transition. Within the domain conventionally designated as the inertial range, we identify two statistically distinct subranges. At larger scales ( R 2 ; 200–6000, d i ), the average eddy displays a field-aligned, tube-like morphology. An inverse correlation is observed between alignment angle and gradient intensity, and the conditional structure-function exponents ζ n —measured perpendicular to both the local mean field and fluctuation direction—agree with the predictions of B. D. G. Chandran et al. and A. Mallet &amp; A. A. Schekochihin, although the parallel and displacement components show more concave scaling than anticipated. At smaller scales ( R 1 ; 10–100, d i ), spectra steepen, eddies become ribbon-like, and intermittency weakens. Within a narrow interval near the ion characteristic scales, eddies approach isotropy before the trend of increasing anisotropy resumes at smaller scales. Analysis using five-point increments further demonstrates a stronger multifractal character at kinetic scales than is resolved with conventional two-point methods. Finally, we discuss the influence of solar wind expansion, finite cross helicity, “anomalous coherence,” and the emergence of a “helicity barrier” in modifying CB/SDDA phenomenology and shaping the statistical properties of solar wind turbulence.