A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer Research Article First Online: 24 May 2011 Received: 13 January 2011 Revised: 19 April 2011 Accepted: 30 April 2011 DOI :
10.1007/s00348-011-1117-z

Cite this article as: LeHew, J., Guala, M. & McKeon, B.J. Exp Fluids (2011) 51: 997. doi:10.1007/s00348-011-1117-z Abstract 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 Re _{τ} = 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.

M. Guala worked on this project at the California Institute of Technology but is currently at the University of Minnesota.

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