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Linear instability analysis of low-$Re$ incompressible flow over a long rectangular finite-span open cavity

Published online by Cambridge University Press:  21 June 2016

Qiong Liu ,
Francisco Gómez Open the ORCID record for Francisco Gómez [Opens in a new window]  and
Vassilios Theofilis
Qiong Liu
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, Madrid, Spain
Francisco Gómez
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, Victoria 3800, Australia
Vassilios Theofilis*
Affiliation:
School of Aeronautics, Universidad Politécnica de Madrid, Madrid, Spain School of Engineering, University of Liverpool, Browlow Hill, Liverpool L69 3GH, UK
*
†Email address for correspondence: [email protected]
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Abstract

TriGlobal linear instability analysis and direct numerical simulations have been performed to unravel the mechanisms ultimately responsible for transition of steady laminar flow over a long rectangular finite-span open cavity with dimensions $L$ : $D$ : $W$$=$ 6 : 1 : 2 to unsteadiness. The steady laminar three-dimensional flow loses stability at $\mathit{Re}_{D,cr}\approx 1080$ as a consequence of linear amplification of a travelling eigenmode that is qualitatively analogous to the shear-layer mode known from analyses of flow in spanwise-periodic cavities, but has a three-dimensional structure which is strongly influenced by the cavity lateral walls. Differences in the eigenspectrum of the present and the spanwise homogeneous flow configuration are documented. Topological changes exerted on the steady laminar flow by linear amplification of the unstable shear-layer mode are reminiscent of observations in experiments at an order of magnitude higher Reynolds number.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , R2
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Copyright
© 2016 Cambridge University Press 

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