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Abstract:
We propose a method to evaluate the Doppler shift and broadening using magnetic field data in solar wind
turbulence. A model of the energy spectrum is constructed in the wavenumber-frequency domain in the direction
of the mean flow, and it is compared with that determined directly from four-point magnetic field data of Cluster
spacecraft using the method of least square fitting. The model assumes the frequencies and wavelengths are
low enough, and long enough, to be in the inertial range of turbulence. The comparison gives the result that
the Doppler shift is consistent with that expected from the measurement of ion bulk speed, whereas the Doppler
broadening is not small but far larger than the root-mean-square of ion bulk speed fluctuation possibly due to
large-scale counter-propagating waves. Measurement of the Doppler shift can be used as an independent method
to determine the mean flow speed, and that of Doppler broadening as a method to evaluate Taylor’s frozen-in flow
hypothesis. The finite Doppler broadening also implies that Taylor’s hypothesis is invalid even at low frequencies
in the solar wind.
