Error estimate of Taylor's frozen-in flow hypothesis in the spectral domain

Abstract

The quality of Taylor's frozen-in flow hypothesis can be measured by estimating the amount of the fluctuation energy mapped from the streamwise wavenumbers onto the Doppler-shifted frequencies in the spectral domain. For a random sweeping case with a Gaussian variation of the large-scale flow, the mapping quality is expressed by the error function which depends on the mean flow speed, the sweeping velocity, the frequency bin, and the frequency of interest. Both hydrodynamic and magnetohydrodynamic treatments are presented on the error estimate of Taylor's hypothesis with examples from the solar wind measurements.