Evolution of MHD turbulence in the expanding solar wind: residual energy and intermittency

TL;DR

This study uses 3D MHD simulations with an expanding box model to investigate how solar wind turbulence evolves, focusing on residual energy, intermittency, and their dependence on initial conditions and expansion effects.

Contribution

It introduces the expanding box model to simulate solar wind turbulence, revealing the consistent generation of negative residual energy and its relation to intermittency and scale-dependent processes.

Findings

Negative residual energy is generated regardless of initial conditions.

Residual energy predominantly distributes in the perpendicular direction, following specific scaling laws.

Intermittency increases with expansion, but its causal link to residual energy is weak.

Abstract

We conduct 3D magnetohydrodynamic (MHD) simulations of decaying turbulence in the solar wind context. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counter-propagating Alfv\'en waves and exhibits an isotropic power spectrum. Our findings reveal the consistent generation of negative residual energy whenever nonlinear interactions are present, independent of the normalized cross helicity $\sigma_c$ and compressibility. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with $[S_2(\mathbf{b})-S_2(\mathbf{u})] \propto l_\perp$ or equivalently $-E_r \propto k_\perp^{-2}$. Here $S_2(\mathbf{b})$ and $S_2(\mathbf{u})$ are second-order structure functions of magnetic field and velocity respectively. In most runs, $S_2(\mathbf{b})$ develops a scaling relation $S_2(\mathbf{b}) \propto l_\perp^{1/2}$ ($E_b \propto k_\perp^{-3/2}$). In contrast, $S_2(\mathbf{u})$ is consistently shallower than $S_2(\mathbf{b})$, which aligns with in-situ observations of the solar wind. We observe that the higher-order statistics of the turbulence, which act as a proxy for intermittency, depend on the initial $\sigma_c$ and are strongly affected by the expansion effect. Generally, the intermittency is more pronounced when the expansion effect is present. Finally, we find that in our simulations although the negative residual energy and intermittency grow simultaneously as the turbulence evolves, the causal relation between them seems to be weak, possibly because they are generated on different scales.