Spectral Anisotropy in 2D plus Slab Magnetohydrodynamic Turbulence in the Solar Wind and Upper Corona

Abstract

The 2D + slab superposition model of solar wind turbulence has its theoretical foundations in nearly incompressible magnetohydrodynamics (NI MHD) in the plasma beta ∼1 or ≪1 regimes. Solar wind turbulence measurements show that turbulence in the inertial range is anisotropic, for which the superposition model offers a plausible explanation. We provide a detailed theoretical analysis of the spectral characteristics of the Elsässer variables in the 2D + NI/slab model. We find that (1) the majority 2D component has a power spectrum in perpendicular wavenumber k ⊥; (2) the strongly imbalanced minority NI/slab turbulence has power spectra and , where k z is aligned with the mean magnetic field; (3) NI/slab turbulence can exhibit a double-power-law spectrum, with the steeper part being G*(k) ∼ k −5/3 and corresponding to strong turbulence and the flatter spectrum satisfying G*(k) ∼ k −3/2 and corresponding to weak turbulence; (4) there is a critical balance regime for NI/slab turbulence that satisfies and ; and (5) the forward and backward Elsässer power spectra can have different spectral forms provided that the triple-correlation times for each are different. We use the spectral analysis to compute the total power spectra in frequency parallel to the solar wind flow for the superposition model, showing that strongly imbalanced turbulence yields an f −5/3 spectrum for all angles between the mean flow and magnetic field, and that double power laws are possible when the nonlinear and Alfvén timescales are both finite.

Turbulence Upstream and Downstream of Interplanetary Shocks

“…The scaling laws of power spectral densities of the physical fields (N, B, V, T) and the relevant anisotropies inferred from spacecraft observations (e.g., [13,28,115,130]), or state-of-the-art computer simulations (see, [40]; and references therein) serve as key factors in understanding the dynamics of the inertial range. Specifically, they can answer the question which turbulent framework [98,144,149] is consistent with observations. It is believed that the dissipative processes that are responsible for the heating of the solar wind act at the sub-ion range.…”

“…The nonlinear interaction between counter streaming Alfvén waves of similar wavelengths is responsible for the generation of Alfvén waves with smaller wavelengths, i.e., the energy within the Alfvénic fluctuations is transferred to smaller scales and the fluctuations become gradually more anisotropic [120]. Furthermore, observations of [9,39,85] supported by theoretical works of [143,144] suggest that solar wind fluctuations are dominated by quasi-2D turbulent fluctuations with a minority "slab" component, meaning that there are two populations of fluctuations, the first have their wave vectors parallel to the background magnetic field, B 0 , while the second have the wave vectors perpendicular to B 0 . The ratio of energies residing within the quasi-2D and slab fluctuations is roughly 4 : 1 (e.g., [9].…”

Evolution of anisotropic turbulence in the fast and slow solar wind: Theory and Solar Orbiter measurements

“…where m p is the proton mass, n s is the solar wind proton density, α is a von-Kármán Taylor constant, and M t A0 (= 0.1) is the turbulent Alfvén Mach number. The terms inside the [...] correspond to the dissipation of quasi-2D turbulence and NI/slab turbulence, in which the last term is related to the Alfvén effect in the NI/slab turbulence, and is derived using NI/slab time-scale introduced by Zank et al (2020). This term vanishes for the unidirectional Alfvén waves (σ * c = ±1; Adhikari et al 2019).…”

“…Anisotropy takes different forms, such as in that i) the power spectral indices can differ for parallel k || and perpendicular k ⊥ wavenumbers with respect to the mean magnetic field (Horbury et al 2008;Podesta 2009;Wicks et al 2010;Narita et al 2010;Bruno & Telloni 2015), ii) the power differs in parallel and perpendicular fluctuations (Montgomery 1982;Matthaeus et al 1990;Bieber et al 1996;Milano et al 2004;Ruiz et al 2011;Pine et al 2020), and iii) the correlation functions differ in directions parallel and perpendicular to the mean magnetic field (Dasso et al 2005;Matthaeus et al 2005;Dasso et al 2008;Weygand et al 2009;Osman & Horbury 2007;Wang et al 2019). Anisotropy has been studied theoretically and numerically (Montgomery & Turner 1981;Shebalin et al 1983;Grappin 1986;Zank & Matthaeus 1992a,b, 1993Grappin et al 1993;Goldreich & Sridhar 1995;Ghosh et al 1998;Dong et al 2014;Verdini & Grappin 2015Zank et al 2017Zank et al , 2020Adhikari et al 2017b). Pine et al (2020), using two approaches, calculated the anisotropy of magnetic field fluctuations in the inertial range from 1 to 45 au using Voyager and Advanced Composition Explorer (ACE) observations.…”

Anisotropy of Magnetic Field and Velocity Fluctuations in the Solar Wind

“…Solar wind measurements reveal the existence of two wavevector geometries of turbulent fluctuations (e.g., Matthaeus et al 1990;Zank & Matthaeus 1992Tu & Marsch 1994;Bieber et al 1996;Podesta & Gary 2011;He et al 2012;Zank et al 2017Zank et al , 2020. Using abbreviations k ⊥ and k P for perpendicular and parallel wavevector components, the first geometry consists of oblique fluctuations with k ⊥ > k P and the second geometry exhibits fluctuations that are more field aligned (k ⊥ < k P ) with lower amplitudes.…”