Non-Dynamic Alignment in Magnetohydrodynamic Turbulence

Abstract

Dynamic alignment in MHD turbulence is commonly interpreted as a tendency of Elsässer increments to align toward smaller inertial-range scales. This interpretation is based on the amplitude-weighted diagnostic \(\langle A_r\sinθ_r\rangle/\langle A_r\rangle\), where \(A_r\) is the product of the two increment amplitudes and \(θ_r\) is the unweighted folded angle. We show that a decrease of the weighted angle toward smaller scales does not require dynamical alignment but can arise from a retention effect in measurements. At fixed scale, larger amplitudes correlate with smaller angles, making the weighted angle smaller than the unweighted angle without implying that the angular population evolves toward alignment with scale. The same covariance-driven reweighting structure underlies the Price equation in evolutionary biology. Applied here in scale space, it separates angular evolution from redistribution of amplitude weight: a lower measured weighted angle at smaller scales can reflect reweighting even when the unweighted angle remains nearly scale independent. In physical time, the picture predicts that, after matching initial amplitudes, high-amplitude large-angle fluctuations lose a larger amplitude fraction over finite lags than high-amplitude small-angle fluctuations, favoring intense small-angle events in weighted statistics. This retention picture allows perpendicular rms Elsässer increments to scale as \(\ell_\perp^{1/4}\), corresponding to an effective \(k_\perp^{-3/2}\) spectrum, without requiring dynamic alignment of typical fluctuations. We test these results using the Johns Hopkins Turbulence Database and NASA Wind measurements. Mean logarithmic increment amplitudes give steeper typical-amplitude slopes than rms-amplitude fits in both datasets, showing stronger sensitivity of second-order statistics to intermittent intense events.