Non-virialized dark-matter axions may be present in the Milky Way halo in the form of low-velocity-dispersion flows. The Axion Dark Matter eXperiment performed a search for the conversion of these axions into microwave photons using a resonant cavity immersed in a strong, static magnetic field. The spread of photon energy in these measurements was measured at spectral resolutions of the order of 1 Hz and below. If the energy variation were this small, the frequency modulation of any real axion signal due to the orbital and rotational motion of the Earth would become non-negligible. Conservative estimates of the expected signal modulation were made and used as a guide for the search procedure. The photon frequencies covered by this search are 812$-$852 and 858$-$892 MHz, which correspond to an axion mass of 3.36$-$3.52 and 3.55$-$3.69 {mu}eV. No axion signal was found, and limits were placed on the maximum local density of non-virialized axions of these masses.
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