Turbulent regimes in collisions of 3D Alfvén-wave packets (2207.04301v2)

Abstract: Using 3D gyrofluid simulations, we revisit the problem of Alfven-wave (AW) collisions as building blocks of the Alfvenic cascade and their interplay with magnetic reconnection at magnetohydrodynamic (MHD) scales. Depending on the large-scale nonlinearity parameter $\chi_0$ (the ratio between AW linear propagation time and nonlinear turnover time), different regimes are observed. For strong nonlinearities ($\chi_0\sim1$), turbulence is consistent with a dynamically aligned, critically balanced cascade--fluctuations exhibit a scale-dependent alignment $\sin\theta_k\propto k_\perp^{-1/4}$, a $k_\perp^{-3/2}$ spectrum and $k_|\propto k_\perp^{1/2}$ spectral anisotropy. At weaker nonlinearities (small $\chi_0$), a spectral break marking the transition between a large-scale weak regime and a small-scale $k_\perp^{-11/5}$ tearing-mediated range emerges, implying that dynamic alignment occurs also for weak nonlinearities. At $\chi_0<1$ the alignment angle $\theta_{k_\perp}$ shows a stronger scale dependence than in the $\chi_0\sim1$ regime, i.e. $\sin\theta_k\propto k_\perp^{-1/2}$ at $\chi_0\sim0.5$, and $\sin\theta_k\propto k_\perp^{-1}$ at $\chi_0\sim0.1$. Dynamic alignment in the weak regime also modifies the large-scale spectrum, scaling roughly as $k_\perp^{-3/2}$ for $\chi_0\sim0.5$ and as $k_\perp^{-1}$ for $\chi_0\sim0.1$. A phenomenological theory of dynamically aligned turbulence at weak nonlinearities that can explain these spectra and the transition to the tearing-mediated regime is provided; at small $\chi_0$, the strong scale dependence of the alignment angle combines with the increased lifetime of turbulent eddies to allow tearing to onset and mediate the cascade at scales that can be larger than those predicted for a critically balanced cascade by several orders of magnitude. Such a transition to tearing-mediated turbulence may even supplant the usual weak-to-strong transition.

• The paper identifies distinct turbulence regimes in 3D Alfvén-wave packet collisions, based on the nonlinearity parameter (χ₀) that differentiates strong and weak turbulent states.
• It employs 3D gyro-fluid simulations to reveal scale-dependent dynamic alignment and spectral anisotropy, confirming a k⊥⁻³/² spectrum in strong turbulence and a tearing-mediated transition at weak nonlinearity.
• The findings have significant implications for energy dissipation and turbulent heating in space and astrophysical plasmas, highlighting the need to incorporate tearing-mediated processes in future plasma models.

Turbulent Regimes in Collisions of 3D Alfvén-Wave Packets

The paper explores the interactions of three-dimensional Alfvén-wave packets and their contribution to the Alfvénic turbulent cascade at magnetohydrodynamic scales, with a focus on the complex interplay with magnetic reconnection. Alfvén-wave collisions are crucial components of MHD turbulence, which inherently exhibits anisotropy along the mean magnetic field. The investigation leverages three-dimensional gyro-fluid simulations to delineate different turbulent regimes based on the nonlinearity parameter, $\chi_0$, which quantifies the balance between linear and nonlinear dynamics.

The paper distinguishes several regimes:

1. Strong Nonlinearity ($\chi_0 \approx 1$): At this regime, turbulence achieves a dynamically aligned, critically balanced state, characterized by a scale-dependent alignment $\sin \theta_{k_\perp} \propto k_\perp^{-1/4}$. The resultant energy spectrum follows a $k_\perp^{-3/2}$ law, and spectral anisotropy is observed as $k_\|\propto k_\perp^{1/2}$. This behavior is consistent with predictions for strong turbulence, where dynamic alignment is considered a mediating factor in energy cascade.
2. Weak Nonlinearity ($\chi_0 < 1$): At lower $\chi_0$ values, the paper identifies a transition to a tearing-mediated range, as evidenced by a spectral break. In these regimes, alignment strengthens with decreasing scale. For instance, at $\chi_0 \approx 0.5$, the alignment scales as $\sin\theta_{k_\perp} \propto k_\perp^{-1/2}$, and at $\chi_0 \approx 0.1$, it follows $\sin\theta_{k_\perp}\propto k_\perp^{-1}$. These findings suggest that dynamic alignment at weak nonlinearities modifies the large-scale spectrum and supports a transition from weak to tearing-mediated regimes.

The implications of this transition to a tearing-mediated regime are notable. Traditional views of MHD turbulence anticipate a progression from weak to strong turbulence; however, this paper indicates that tearing can initiate prior to reaching critical balance, depending more heavily on the nonlinearity parameter and initial conditions. Tearing-mediated turbulence is marked by a $k_\perp^{-11/5}$ spectrum, showcasing different alignment properties than a critically balanced cascade.

Implications and Future Directions

The implications of these findings extend to our understanding of energy dissipation and turbulent heating in space and astrophysical plasmas, particularly in environments with varying degrees of nonlinearity. The alteration of cascade dynamics at weak nonlinearities highlights the necessity to consider tearing-mediated processes in models of plasma turbulence.

For future exploration, investigating the implications of these tearing-mediated transitions on cosmic ray scattering in environments with low Alfvén speeds could be critically important. Moreover, although the current paper does not specifically account for effects like imbalance and residual energy, incorporating these factors into future models could enhance understanding of plasma dynamics in both controlled and naturally occurring systems.

Overall, this work provides valuable insights into the multiscale behavior of turbulent plasmas and suggests that even weak turbulence can have a profound influence on the spectral characteristics and energy dissipation mechanisms of the system.