Space–time structure and wavevector anisotropy in space plasma turbulence

Space and astrophysical plasmas often develop into a turbulent state and exhibit nearly random and stochastic motions. While earlier studies emphasize more on understanding the energy spectrum of turbulence in the one-dimensional context (either in the frequency or the wavenumber domain), recent achievements in plasma turbulence studies provide an increasing amount of evidence that plasma turbulence is essentially a spatially and temporally evolving phenomenon. This review presents various models for the space-time structure and anisotropy of the turbulent fields in space plasmas, or equivalently the energy spectra in the wavenumber-frequency domain for the space-time structures and that in the wavevector domain for the anisotropies. The turbulence energy spectra are evaluated in different one-dimensional spectral domains; one speaks of the frequency spectra in the spacecraft observations and the wavenumber spectra in the numerical simulation studies. The notion of the wavenumber-frequency spectrum offers a more comprehensive picture of the turbulent fields, and good models can explain the one-dimensional spectra in the both domains at the same time. To achieve this goal, the Doppler shift, the Doppler broadening, linear-mode dispersion relations, and sideband waves are reviewed. The energy spectra are then extended to the wavevector domain spanning the directions parallel and perpendicular to the large-scale magnetic field. By doing so, the change in the spectral index at different projections onto the one-dimensional spectral domain can be explained in a simpler way.