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Nonlinear dynamics near the stability margin in rotating pipe flowThe 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 the entire marginal stability boundary is explored. 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 traveling 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 traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.
Document ID
19920037335
Document Type
Reprint (Version printed in journal)
Authors
Yang, Z. (NASA Lewis Research Center Cleveland, OH; Cornell University, Ithaca, NY, United States)
Leibovich, S. (Cornell University Ithaca, NY, United States)
Date Acquired
August 15, 2013
Publication Date
December 1, 1991
Publication Information
Publication: Journal of Fluid Mechanics
Volume: 233
ISSN: 0022-1120
Subject Category
FLUID MECHANICS AND HEAT TRANSFER
Funding Number(s)
CONTRACT_GRANT: AF-AFOSR-89-0346
Distribution Limits
Public
Copyright
Other