Purely helical absolute equilibria and chirality of (magneto)fluid turbulence

Abstract

Purely helical absolute equilibria of incompressible neutral fluids and plasmas (electron, singlefluid and two-fluid magnetohydrodyanmics) are systematically studied with the help of helical (wave) representation and truncation, for genericities and specificities about helicity. A unique chirality selection and amplification mechanism and relevant insights, such as the one-chiralsector-dominated states, among others, about (magneto)fluid turbulence follow.

Chirality, extended magnetohydrodynamics statistics and topological constraints for solar wind turbulence

“…Our main point is that the two extreme values ±1 for Pm found in the above are for linear waves, which themselves may not be appropriate in the case of their simulation without a guide field B0 (though large-scale magnetic fluctuations might be coarsegrained to be a local guide field, the situation would be much more complicated), and may not be appropriate for characterizing eMHD and iMHD turbulence. But, the insight that the turbulence is dominated by the iMHD and eMHD flow respectively at subsequent scale regimes, which may be termed one-flow-dominated state (OFDS), is valuable and the proper nonlinear theory may be a combination of the one-chiral-sector-dominated state (OCSDS -a state dominated by the '+' or the '-' chiral sector: Zhu, Yang & Zhu 2014) with OFDS: Having neither introduced the mean magnetic field (i.e, B may be just b), nor linearized the models, we have for uni-chiral case, σm = s = −σc, i.e.,…”

“…The usage of linear-wave argument is 'popular' in plasma literatures, which, in many cases are not necessary; for instance, relevant to our notion, it appears to us that the interesting hodographs of He, Tu, Marsch & Yao (2012) for chiral magnetic fluctuations (see also Telloni & Bruno 2016) may not necessarily be related to just linear waves. Note also that OCSDS requires non-vanishing (generalized) helicity (Zhu, Yang & Zhu 2014), whose origin/emergence should also be addressed.…”

“…Note that the decomposition not only physically separates the two chiral sectors, but also exposes the 'mirror symmetries' of the spectral, not to mention that now the denominator is of third order and that the problem can be analytically tracked down to each zeros (poles of the spectra): by "'mirror symmetries' of the spectral" we mean the poles are of opposite signs. With the fact that the pole(s) should be positive (k > 0), one can then figure out all possible shapes of the spectra for physical inference (Zhu, Yang & Zhu 2014). …”

“…An important remark is that we should not take our results only as the chiral decomposition, but also as the 'purely helical' (i.e., uni-chiral at each k) AE which may allow completely novel features, such as that with the new physically relevant temperature parameter(s), the 'negative (energy) temperature' (Zhu, Yang & Zhu 2014), for homochiral Euler, among other possibilities (Zhu 2014). We may apply the chiroids' AE for finer analysis of plasmas dynamics and the SWT.…”

“…The generalized helicities are not only Casimirs, but also quadratic invariant rugged with respect to Galerkin truncations (see later discussions), thus must play important dynamical roles. For example, helicity leads to one-chiral-sector-dominated states (OCSDS: Zhu, Yang & Zhu 2014) in turbulence, whose exposition requires helical-mode representation.…”