Four-dimensional energy spectrum for space-time structure of plasma turbulence

A parametric model of the inertial-range energy spectrum is constructed for plasma turbulence in the four-dimensional wave vector and frequency domain. The model is based on that of the Eulerian wavenumber-frequency spectrum developed for describing fluid turbulence, and includes wave vector anisotropies in the three-dimensional wave vector domain by approximating the spectrum to a set of ellipses. The shape of the four-dimensional spectrum is determined by the Doppler shift, the Doppler broadening, and anisotropy coefficients. The model is applied to the magnetic energy spectrum in the near-Earth solar wind measured by four Cluster spacecraft, and the set of the spectral parameters are determined observationally. In this way, space-time structure of plasma turbulence can be condensed into a small number of parameters, which is suitable for evaluating the energy spectra in observational and numerical studies on the quantitative basis.