Spectral Assessment of the Turbulent Convection Velocity in a Spatially Developing Flat Plate Turbulent Boundary Layer at Reynolds Number \(Re_\theta = 13\,000\)
A method inspired by del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009,  is derived to assess the wavelength-dependent convection velocity in a zero pressure gradient spatially developing flat plate turbulent boundary layer at \(Re_\theta = 13\,000\) for all wavelengths and all wall distances, using only estimates of the time power spectral density of the streamwise velocity and of its local spatial derivative. The resulting global convection velocity has a least-squares interpretation and is easily related to the wavelength-dependent convection velocity. The method intrinsically provides an estimation of the validity of Taylor’s hypothesis by a correlation coefficient identical to the one from del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009, . The results reveal some similarities between the convection of the superstructures, the hairpin packets, and the near-wall structures. The convection velocity of the superstructures is isolated by restricting the global convection velocity to the largest wavelengths. The spatial spectrum is estimated from the temporal spectrum using the frequency-dependent convection velocity. The results are consistent with a classical correlation-based evaluation.
KeywordsHigh Reynolds Number Streamwise Velocity Convection Velocity Coherent Motion Dilatation Factor
This work was performed using HPC resources from GENCI-CINES (Project ZDESWALLTURB, Grant 2012-[c2012026817]). The authors wish to thank Pierre-Élie Weiss and Romain Laraufie for fruitful discussions. All the people involved in the evolution of the FLU3M code are warmly acknowledged. The thesis of Nicolas Renard is partly funded by the French defense procurement agency DGA.
- 1.C. Atkinson, N. Buchmann, O. Amili, J. Soria, High-resolution large field-of-view experimental investigation of turbulent convection velocities in a turbulent boundary layer. in International Symposium on Turbulence and Shear Flow Phenomena (TSFP-8) (2013)Google Scholar
- 13.R. de Kat, L. Gan, J.R. Dawson, B. Ganapathisubramani, Limitations of estimating turbulent convection velocities from PIV, in 16th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal (2012)Google Scholar
- 17.C.C. Lin, On Taylor’s hypothesis and the acceleration terms in the Navier-Stokes equations. Q. Appl. Math. X(4), 154–165 (1953)Google Scholar