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Instabilities of plane Poiseuille flow with a streamwise system rotation

Published online by Cambridge University Press:  30 April 2008

S. MASUDA ,
S. FUKUDA  and
M. NAGATA
S. MASUDA
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan
S. FUKUDA
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan
M. NAGATA
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan
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Abstract

We analyse the stability of plane Poiseuille flow with a streamwise system rotation. It is found that the instability due to two-dimensional perturbations, which sets in at the well-known critical Reynolds number, Rc = 5772.2, for the non-rotating case, is delayed as the rotation is increased from zero, showing a stabilizing effect of rotation. As the rotation is increased further, however, the laminar flow becomes most unstable to perturbations which are three-dimensional. The critical Reynolds number due to three-dimensional perturbations at this higher rotation case is many orders of magnitude less than the corresponding value due to two-dimensional perturbations. We also perform a nonlinear analysis on a bifurcating three-dimensional secondary flow. The secondary flow exhibits a spiral vortex structure propagating in the streamwise direction. It is confirmed that an antisymmetric mean flow in the spanwise direction is generated in the secondary flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 603 , 25 May 2008 , pp. 189 - 206
Copyright
Copyright © Cambridge University Press 2008

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References

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