*Earth Planets Space,* Vol. 65 (No. 1), pp. e5-e8, 2013

doi:10.5047/eps.2012.12.002

*E-LETTER*
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Doppler shift and broadening in solar wind turbulence

Y. Narita^{1}, K.-H. Glassmeier^{2,3}, U. Motschmann^{4,5}, and M. Wilczek^{6}

^{1}Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, A-8042 Graz, Austria

^{2}Institut für Geophysik und extraterrestrische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, D-38106, Germany

^{3}Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau, Germany

^{4}Institut für Theoretische Physik, Technische Universität Braunschweig, Mendelssohnstr. 3, D-38106, Germany

^{5}Deutsches Zentrum für Luft- und Raumfahrt, Institut für Planetenforschung, Rutherfordstr. 2, D-12489 Berlin, Germany

^{6}Institut für Theoretische Physik, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany

(Received October 31, 2012; Revised December 11, 2012; Accepted December 13, 2012; Online published January 31, 2013)

**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.

**Key words: **
Doppler shift, Doppler broadening, wavenumber-frequency spectrum, multi-spacecraft measurements.

Corresponding author E-mail: yasuhito.narita@oeaw.ac.at

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