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On the secondary instabilities of transient growth in Couette flow

Published online by Cambridge University Press:  20 January 2017

Michael Karp  and
Jacob Cohen
Michael Karp*
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Jacob Cohen
Affiliation:
Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: mkarp@technion.ac.il
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Abstract

The secondary instability of linear transient growth (TG) in Couette flow is explored theoretically, utilizing an analytical representation of the TG based on four modes and their nonlinear interactions. The evolution of the secondary disturbance is derived using the multiple time scales method. The theoretical predictions are compared with direct numerical simulations and very good agreement with respect to the growth of the disturbance energy and associated vortical structures is observed, up to the final stage just before the breakdown to turbulence. The theoretical model enables us to perform a full parametric study, including TG symmetry type, various wavenumbers, initial energy, TG nonlinearity and Reynolds number, to find all possible routes to transition and the optimal parameters for each type of the secondary disturbance. It is found that the most dangerous secondary disturbances are associated with spanwise wavenumbers which generate the strongest inflection points, i.e. those having maximal shear, rather than with those maximizing the energy gain during the TG phase.

JFM classification

Instability: Instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 528 - 557
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Copyright
© 2017 Cambridge University Press 

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