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.

空间和天体物理等离子体经常发展成湍流状态并表现出近乎随机和随机的运动。虽然早期的研究更多地强调了解一维背景下的湍流能谱（无论是频率域还是波数域），但等离子体湍流研究的最新成就提供了越来越多的证据，表明等离子体湍流本质上是空间和时间上的湍流。不断发展的现象。这篇综述提出了空间等离子体中的时空结构和湍流场各向异性的各种模型，或者等效地，时空结构的波数频域中的能谱和各向异性的波矢域中的能谱。在不同的一维谱域中评估湍流能谱；一是航天器观测中的频谱和数值模拟研究中的波数谱。波数-频率谱的概念提供了湍流场的更全面的图像，好的模型可以同时解释两个域中的一维谱。为了实现这一目标，回顾了多普勒频移、多普勒展宽、线性模式色散关系和边带波。然后将能谱扩展到跨越平行和垂直于大尺度磁场的方向的波矢量域。通过这样做，可以以更简单的方式解释在一维谱域上不同投影处的谱指数的变化。