Anisotropy in solar wind plasma turbulence

Abstract

A review of spectral anisotropy and variance anisotropy for solar wind fluctuations is given, with the discussion covering inertial range and dissipation range scales. For the inertial range, theory, simulations and observations are more or less in accord, in that fluctuation energy is found to be primarily in modes with quasi-perpendicular wavevectors (relative to a suitably defined mean magnetic field), and also that most of the fluctuation energy is in the vector components transverse to the mean field. Energy transfer in the parallel direction and the energy levels in the parallel components are both relatively weak. In the dissipation range, observations indicate that variance anisotropy tends to decrease towards isotropic levels as the electron gyroradius is approached; spectral anisotropy results are mixed. Evidence for and against wave interpretations and turbulence interpretations of these features will be discussed. We also present new simulation results concerning evolution of variance anisotropy for different classes of initial conditions, each with typical background solar wind parameters.

Keywords: anisotropy; turbulence; waves.

Figure 1.

Fourier space regions associated with MHD turbulence models and phenomenologies. (a) Slab+2D. (b) Critical balance and the equal time-scale curve. (c) Quasi-two-dimensional fluctuations+wave-like fluctuations, with the arrows indicating typical directions of spectral energy transfer; transfer within and between regions involves at least somewhat different physics. (Online version in colour.)

Figure 2.

(a) Wavevector anisotropy from 1 AU study by Podesta [60]. P_⊥ and P_∥ are the reduced magnetic spectra in angular bins close to the k_⊥ and k_∥ axes. Copyright AAS. Reproduced with permission. (b) Observational (1 AU) frequency–wavenumber pairs (circles) and linear theory dispersion relations for KAWs and fast modes with wavevectors at the stated angles (solid curves). Dashed curves are associated linear theory damping rates, γ. Highly oblique KAWs are not inconsistent with the data, but the data are also consistent with low-frequency quasi-two-dimensional turbulence. Reprinted with permission from Sahraoui et al. [67]. Copyright 2010 © American Physical Society. (Online version in colour.)

Figure 3.

Magnetic compressibility versus wavenumber from a Kiyani et al. [102] study at 1 AU. Local mean fields are typically employed, although a comparison with an analysis based on the global field is also shown, along with some linear Vlasov theory results. In the dissipation range, note the tendency towards isotropy with decreasing length scale. Copyright AAS. Reproduced with permission. (Online version in colour.)

Figure 4.

Variance anisotropy quantities from compressible three-dimensional MHD simulations. Each row is for a β_p=1 run with a different type of IC. Top: b,v strictly toroidal. Middle: isotropic, meaning b,v have equal power in the toroidal and poloidal components. Bottom: b isotropic, v purely longitudinal. (Online version in colour.)