On the violation of the zeroth law of turbulence in space plasmas

Abstract

The zeroth law of turbulence states that, for fixed energy input into large-scale motions, the statistical steady state of a turbulent system is independent of microphysical dissipation properties. This behaviour, which is fundamental to nearly all fluid-like systems from industrial processes to galaxies, occurs because nonlinear processes generate smaller and smaller scales in the flow, until the dissipation – no matter how small – can thermalise the energy input. Using direct numerical simulations and theoretical arguments, we show that in strongly magnetised plasma turbulence such as that recently observed by the Parker Solar Probe spacecraft, the zeroth law is routinely violated. Namely, when such turbulence is ‘imbalanced’ – when the large-scale energy input is dominated by Alfvénic perturbations propagating in one direction (the most common situation in space plasmas) – nonlinear conservation laws imply the existence of a ‘barrier’ at scales near the ion gyroradius. This causes energy to build up over time at large scales. The resulting magnetic-energy spectra bear a strong resemblance to those observed in situ, exhibiting a sharp, steep kinetic transition range above and around the ion-Larmor scale, with flattening at yet smaller scales. The effect thus offers a possible solution to the decade-long puzzle of the position and variability of ion-kinetic spectral breaks in plasma turbulence. The existence of the ‘barrier’ also suggests that, how a plasma is forced at large scales (the imbalance) may have a crucial influence on thermodynamic properties such as the ion-to-electron heating ratio.

The In Situ Signature of Cyclotron Resonant Heating

“…Fully kinetic simulations in the presence of such a barrier [82] show the generation of quasi-parallel cyclotron modes, similar to those observed in the solar wind. This barrier to imbalanced energy flux [82,88] provides a novel method for generating cyclotron waves that can dissipate imbalanced turbulence that is consistent with a variety of observations [58,59,78,[89][90][91][92][93]. Further work is required to understand the origin of cyclotron waves and their connection to turbulence.…”

“…However, recent work suggests that imbalance, i.e. the dominance of the outward Alfvén mode, may prevent energy from cascading to kinetic scales [88]. Fully kinetic simulations in the presence of such a barrier [82] show the generation of quasi-parallel cyclotron modes, similar to those observed in the solar wind.…”

Anisotropy of Solar Wind Turbulence in the Inner Heliosphere at Kinetic Scales: PSP Observations

“…The dispersive kinetic waves allow nonlinear interaction between the copropagating wave packets, which can lead to a steepened transition range at ion scales, but the required imbalance for α t < − 3.5 is much stronger than the observation (Voitenko & Keyser 2016). On the other hand, there is a proposed "helicity barrier" from the finite-Larmorradius MHD in β p = 1 plasma near the ion scales preventing the energy cascading to the smaller scales (Meyrand et al 2021). Only a small portion of energy would leak through the barrier and produce a steep transition range.…”

“…Sometimes a sharp transition range is observed with α t ∼ 4 (Sahraoui et al 2010;Bowen et al 2020a). This transition range may be caused by imbalanced turbulence (Voitenko & Keyser 2016;Meyrand et al 2021), energy dissipation of kinetic waves (Howes et al 2008), ion-scale coherent structures (Lion et al 2016), or a reconnection dominated range (Mallet et al 2017). At smaller scales, a flatter sub-ion kinetic range forms with the spectral index α k ∼ 7/3, which can be explained as the MHD Alfvénic turbulence developing into a type of kinetic wave turbulence, e.g., kinetic Alfvén waves (KAWs; Schekochihin et al 2009) or whistler waves (Cho & Lazarian 2004).…”

Reconnection-controlled decay of magnetohydrodynamic turbulence and the role of invariants

“…In summary, the Saffman-type-invariant approach appears to be an extremely useful tool for describing the decay of turbulence subject to the conservation of signindefinite invariants. There are many different types of fluid turbulence to which this approach may be usefully applied -a number of them are reviewed in [5], and there are likely to be others, especially in a large variety of plasma systems increasingly of interest in the context of various types of space or astrophysical turbulence (see, e.g., [52][53][54]). In the physical systems where frozenin magnetic fields are dominant actors in the dynamics, magnetic reconnection is likely to be the key physical process whereby the decay occurs.…”