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Transition to turbulence over convex surfaces

Published online by Cambridge University Press:  25 September 2018

Michael Karp Open the ORCID record for Michael Karp [Opens in a new window]  and
M. J. Philipp Hack Open the ORCID record for M. J. Philipp Hack [Opens in a new window]
Michael Karp*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
M. J. Philipp Hack
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

Although boundary-layer flows over convex surfaces are exponentially stable, non-modal mechanisms may enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instabilities in flows over convex surfaces is performed. The optimal disturbance in the steady case corresponds to alternating streaks and streamwise vortices of opposite sign that reinforce one another due to lift-up and centrifugal forces, respectively. The process repeats with a constant (naturally appearing) streamwise wavelength which is proportional to the square root of the radius. Unsteady disturbances achieve a higher optimal gain, compared to the steady case, as a result of the opposing effects of the lift-up and centrifugal mechanisms. Linear analysis shows that the curvature has a negligible effect on secondary instabilities. Direct numerical simulations of transient growth with and without secondary instabilities confirm the predictions obtained by the local stability theory. It is found that the presence of a secondary instability is not sufficient, on its own, to ensure transition to turbulence. Only sufficiently long and energetic streaks trigger the breakdown to turbulence.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 1208 - 1237
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Copyright
© 2018 Cambridge University Press 

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Karp et al. supplementary movie

Streamwise streaks for case C in table 3, visualized by isosurfaces of _±0.1 streamwise disturbance velocity (positive, red; negative, blue). Flow from left to right.

Download Karp et al. supplementary movie(Video)
Video 7 MB