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Transition in the asymptotic suction boundary layer over a heated plate

Published online by Cambridge University Press:  19 August 2016

Stefan Zammert ,
Nicolas Fischer  and
Bruno Eckhardt
Stefan Zammert*
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628 CD Delft, The Netherlands
Nicolas Fischer
Affiliation:
Fakultät Verkehrswissenschaften “Friedrich List”, Technische Universität Dresden, D-01062 Dresden, Germany
Bruno Eckhardt
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany J.M. Burgerscentrum, Delft University of Technology, 2628 CD Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The asymptotic suction boundary layer (ASBL) is a parallel shear flow that becomes turbulent in a bypass transition in parameter regions where the laminar profile is stable. We here add a temperature gradient perpendicular to the plate and explore the interaction between convection and shear in determining the transition. We find that the laminar state becomes unstable in a subcritical bifurcation and that the critical Rayleigh number and wavenumber depend strongly on the Prandtl number. We also track several secondary bifurcations and identify states that are localized in two directions, showing different symmetries. In the subcritical regime, transient turbulent states which are connected to exact coherent states and follow the same transition scenario as found in linearly stable shear flows are identified and analysed. The study extends the bypass transition scenario from shear flows to thermal boundary layers and highlights the intricate interactions between thermal and shear forces.

JFM classification

Boundary Layers: Boundary Layers Convection: Convection Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 803 , 25 September 2016 , pp. 175 - 199
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Copyright
© 2016 Cambridge University Press 

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Zammert et al. supplementary movie

Dynamics of the temperature field for the periodic orbit $PO_{1}$. Additionally, the temporal evolution of the amplitude $a$ and of the Nusselt number are shown.

Download Zammert et al. supplementary movie(Video)
Video 516.8 KB

Zammert et al. supplementary movie

Dynamics of the temperature field for a trajectory on the chaotic attractor at Ra=9.95. Additionally, the temporal evolution of the amplitude $a$ and of the Nusselt number are shown.

Download Zammert et al. supplementary movie(Video)
Video 681.9 KB

Zammert et al. supplementary movie

Dynamics of the temperature field for a trajectory on the chaotic saddle at Ra=10.2. Additionally, the temporal evolution of the amplitude $a$ and of the Nusselt number are shown.

Download Zammert et al. supplementary movie(Video)
Video 445.7 KB