Time-resolved particle image velocimetry (PIV) measurements performed in wall parallel planes at three wall normal locations, y+ = 34, 108, and 278, in a zero pressure gradient turbulent boundary layer at Reτ = 470 are used to illuminate the distribution of streamwise velocity fluctuations in a three-dimensional energy spectrum (2D in space and 1D in time) over streamwise, spanwise, and temporal wavelengths. Two high-speed cameras placed side by side in the streamwise direction give a 10δ × 5δ streamwise by spanwise field of view with a vector spacing of \(\Updelta x^+ = \Updelta z^+ \approx 37\) and a time step of \(\Updelta t^+=0.5\). Although 3D wavenumber--frequency spectra have been calculated in acoustics studies, to the authors’ knowledge this is the first time they has been calculated and presented for a turbulent boundary layer. The calculation and normalization of this spectrum, its relation to 2D and 1D spectra, and the effects of the PIV algorithm on its shape are carefully analyzed and outlined.
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We would like to acknowledge and thank Prof. Mory Gharib and Dr. David Jeon for their assistance and allowing us to use their free surface water tunnel facility at Caltech in which all the experiments presented were performed. We would also like to acknowledge the Air Force Office of Scientific Research (AFOSR) for their continued support of this research under award number #FA9550-09-1-0701.
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