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Nonlinear dynamics near the stability margin in rotating pipe flow

Published online by Cambridge University Press:  26 April 2006

Z. Yang  and
S. Leibovich
Z. Yang
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Present address: Center for Modeling of Turbulence and Transition, NASA Lewis Research Center/ICOMP, Cleveland, OH 44135, USA.
S. Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and we explore the entire marginal stability boundary. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a travelling wave. The envelope of the wave system is governed by a complex Ginzburg–Landau equation. The Ginzburg–Landau equation admits Stokes waves, which correspond to standing modulations of the linear travelling wavetrain, as well as travelling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 329 - 347
Copyright
© 1991 Cambridge University Press

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