Applicability of Taylor's hypothesis in rough- and smooth-wall boundary layers

Abstract

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number (δ+ ∼ 12 000). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor's frozen turbulence hypothesis (Proc. R. Soc. Lond. A..