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Receptivity, instability and breakdown of Görtler flow

Published online by Cambridge University Press:  11 July 2011

LARS-UVE SCHRADER ,
LUCA BRANDT  and
TAMER A. ZAKI
LARS-UVE SCHRADER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
LUCA BRANDT
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
TAMER A. ZAKI*
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: t.zaki@imperial.ac.uk
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Abstract

Receptivity, disturbance growth and breakdown to turbulence in Görtler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Görtler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Görtler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Görtler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Görtler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Görtler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Görtler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Görtler modes.

JFM classification

Boundary Layers: Boundary layer receptivity Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 362 - 396
Copyright
Copyright © Cambridge University Press 2011

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References

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