Spectral Assessment of the Turbulent Convection Velocity in a Spatially Developing Flat Plate Turbulent Boundary Layer at Reynolds Number \(Re_\theta = 13\,000\)

  • Nicolas RenardEmail author
  • Sébastien Deck
  • Pierre Sagaut
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 23)


A method inspired by del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009, [7] 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, [7]. 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.


High Reynolds Number Streamwise Velocity Convection Velocity Coherent Motion Dilatation Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Nicolas Renard
    • 1
    Email author
  • Sébastien Deck
    • 1
  • Pierre Sagaut
    • 2
  1. 1.Onera, The French Aerospace LabMeudonFrance
  2. 2.Institut Jean le Rond D’AlembertUniversité Pierre Et Marie CurieParisFrance

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