Higher-Order Analysis of Three-Dimensional Anisotropy in Imbalanced Alfv\'enic Turbulence

We analyze in-situ observations of imbalanced solar wind turbulence to evaluate MHD turbulence models grounded in "Critical Balance" (CB) and "Scale-Dependent Dynamic Alignment" (SDDA). At energy injection scales, both outgoing and ingoing modes exhibit a weak cascade; a simultaneous tightening of SDDA is noted. Outgoing modes persist in a weak cascade across the inertial range, while ingoing modes shift to a strong cascade at $\lambda \approx 3 \times 10^{4} d_i$, with associated spectral scalings deviating from expected behavior due to "anomalous coherence" effects. The inertial range comprises two distinct sub-inertial segments. Beyond $\lambda \gtrsim 100 d_i$, eddies adopt a field-aligned tube topology, with SDDA signatures mainly evident in high amplitude fluctuations. The scaling exponents $\zeta_{n}$ of the $n$-th order conditional structure functions, orthogonal to both the local mean field and fluctuation direction, align with the analytical models of Chandran et al. 2015 and Mallet et al. 2017, indicating "multifractal" statistics and strong intermittency; however, scaling in parallel and displacement components is more concave than predicted, possibly influenced by expansion effects. Below $\lambda \approx 100 d_i$, eddies become increasingly anisotropic, evolving into thin current sheet-like structures. Concurrently, $\zeta_{n}$ scales linearly with order, marking a shift towards "monofractal" statistics. At $\lambda \approx 8 d_i$, the increase in aspect ratio halts, and the eddies become quasi-isotropic. This change may signal tearing instability, leading to reconnection, or result from energy redirection into the ion-cyclotron wave spectrum, aligning with the "helicity barrier". Our analysis utilizes 5-point structure functions, proving more effective than the traditional 2-point method in capturing steep scaling behaviors at smaller scales.