Statistical and Temporal Characterization of Turbulent Rayleigh-Bénard Convection Boundary Layers Using Time-Resolved PIV Measurements

  • Christian E. WillertEmail author
  • Ronald du Puits
  • Christian Resagk
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 23)


This contribution reports on near-wall flow field measurements in turbulent Rayleigh-Bénard convection (RBC) in air at a fixed Prandtl number \(\mathrm {Pr} = 0.7\) and Rayleigh number \(\mathrm {Ra} = 1.45 \times 10^{10}\). For the experiment, the large-scale convection (LSC) was confined to a rectangular box of \(2.5 \times 2.5 \times 0.65\,\mathrm {m}^3\) made of transparent acrylic sheets. Prior video-graphic visualizations of the bottom boundary layer flow by means of laser light sheet illumination of small particles indicated the presence of highly dynamic flow behaviour at flow conditions that classical stability analysis predicts to still be in the laminar regime. While theory predicts a transition to turbulence at Reynolds numbers \(\mathrm {Re}_\delta \approx 420\), the present investigation exhibits highly unsteady flow at a much lower Reynolds number of \(\mathrm {Re}_\delta \approx 260\) based on boundary layer thickness. With the help of the PIV data, it can be demonstrated that the entrainment of turbulent structures from the mean wind into the boundary layer acts, alongside with the destabilization due to inner shear, as a second mechanism on its path to turbulence. Both contributions must be considered when predicting the critical bound towards the ultimate regime of thermal convection. The measurements rely on the acquisition of long, continuous sequences of particle image velocimetry (PIV) data from which both statistical and spectral information can be retrieved. Contrary to conventional implementation of the PIV technique the field of view is restricted to a narrow strip, generally extending in wall-normal direction. In this way, both the acquisition frequency and the total number images of the employed high-speed camera are proportionally increased. The temporally oversampled data allows the use of multi-frame PIV processing algorithms which reduce measurement uncertainties with respect to standard dual-frame analysis.


Boundary Layer Particle Image Velocimetry Rayleigh Number Boundary Layer Flow Particle Image Velocimetry Measurement 
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.


  1. 1.
    G. Ahlers, S. Grossmann, D. Lohse, Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Rev. Mod. Phys. 81, 503–537 (2009). doi: 10.1103/RevModPhys.81.503 CrossRefGoogle Scholar
  2. 2.
    R. du Puits, C. Resagk, A. Thess, Mean velocity profile in confined turbulent convection. Phys. Rev. Lett. 99, 234504 (2007). doi: 10.1103/PhysRevLett.99.234504 CrossRefGoogle Scholar
  3. 3.
    R. du Puits, C. Resagk, A. Thess, Structure of viscous boundary layers in turbulent Rayleigh-Bénard convection. Phys. Rev. E 80, 036318 (2009). doi: 10.1103/PhysRevE.80.036318 CrossRefGoogle Scholar
  4. 4.
    R. du Puits, J. Rilk, C. Resagk, A. Thess: Boundary layers in turbulent Rayleigh-Bénard convection in air. (2012). arXiv: 1209.6201v1[physics.fluspsdyn]
  5. 5.
    R. du Puits, C. Resagk, A. Thess, Thermal boundary layers in turbulent Rayleigh-Bénard convection at aspect ratios between 1 and 9. New J. Phys. 15(1), 013040 (2013)CrossRefGoogle Scholar
  6. 6.
    R. du Puits, L. Li, C. Resagk, A. Thess, C. Willert, Turbulent boundary layer in high Rayleigh number convection in air. Phys. Rev. Lett. 112, 124301 (2014). doi: 10.1103/PhysRevLett.112.124301 CrossRefGoogle Scholar
  7. 7.
    M.S. Emran, J. Schumacher, Lagrangian tracer dynamics in a closed cylindrical turbulent convection cell. Phys. Rev. E 82, 016303 (2010). doi: 10.1103/PhysRevE.82.016303 CrossRefGoogle Scholar
  8. 8.
    S. Grossmann, D. Lohse, Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 27–56 (2000). doi: 10.1017/S0022112099007545 MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    R.H. Kraichnan, Turbulent thermal convection at arbitrary prandtl number. Phys. Fluid (1958-1988) 5(11), 1374–1389 (1962). doi: 10.1063/1.1706533 MathSciNetCrossRefGoogle Scholar
  10. 10.
    L. Li, C. Resagk, R. du Puits, Viscous boundary layers in turbulent Rayleigh-Bénard convection. J. Phys.: Conf. Ser. 318(8), 082004 (2011). doi: 10.1088/1742-6596/318/8/082004 Google Scholar
  11. 11.
    N. Shi, M.S. Emran, J. Schumacher, Boundary layer structure in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 706, 5–33 (2012). doi: 10.1017/jfm.2012.207 MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    C. Sun, Y.H. Cheung, K.Q. Xia, Experimental studies of the viscous boundary layer properties in turbulent Rayleigh-Bénard convection. J. Fluid Mech. 605, 79–113 (2008). doi: 10.1017/S0022112008001365 CrossRefzbMATHGoogle Scholar
  13. 13.
    W. Tollmien, Über die Entstehung der Turbulenz. 1. Mitteilung. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse 1929, 21–44 (1929)zbMATHGoogle Scholar
  14. 14.
    M. van Reeuwijk, H.J.J. Jonker, K. Hanjalić, Wind and boundary layers in Rayleigh-Bénard convection. ii. Boundary layer character and scaling. Phys. Rev. E 77, 036312 (2008). doi: 10.1103/PhysRevE.77.036312 CrossRefGoogle Scholar
  15. 15.
    C. Willert, High-speed particle image velocimetry for the efficient measurement of turbulence statistics. Exp. Fluids (submitted)Google Scholar
  16. 16.
    Q. Zhou, K.Q. Xia, Measured instantaneous viscous boundary layer in turbulent Rayleigh-Bénard convection. Phys. Rev. Lett. 104, 104301 (2010). doi: 10.1103/PhysRevLett.104.104301 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Christian E. Willert
    • 1
    Email author
  • Ronald du Puits
    • 2
  • Christian Resagk
    • 2
  1. 1.DLR Institute of Propulsion TechnologyGerman Aerospace CenterKölnGermany
  2. 2.Department of Mechanical EngineeringTechnische Universität IlmenauIlmenauGermany

Personalised recommendations