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Highly optimized transitions to turbulence

Bobba, K. M. and Bamieh, B. and Doyle, J. C. (2002) Highly optimized transitions to turbulence. In: 41st IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 4559-4562. ISBN 0-7803-7516-5.

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We study the Navier-Stokes equations in three dimensional plane Couette flow geometry subject to stream-wise constant initial conditions and perturbations. The resulting two dimensional/three component (2D/3C) model has no bifurcations and is globally (non-linearly) stable for all Reynolds numbers R, yet has a total transient energy amplification that scales like R/sup 3/. These transients also have the particular dynamic flow structures known to play a central role in wall bounded shear flow transition and turbulence. This suggests a highly optimized tolerance (HOT) model of shear flow turbulence, where streamlining eliminates generic bifurcation cascade transitions that occur in bluff body flows, resulting in a flow which is stable to arbitrary changes in Reynolds number but highly fragile in amplifying arbitrarily small perturbations. This result indicates that transition and turbulence in special streamlined geometries is not a problem of linear or nonlinear instability, but rather a problem of robustness.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Bamieh, B.0000-0001-9237-4613
Doyle, J. C.0000-0002-1828-2486
Additional Information:© 2002 IEEE. This work is funded under AFOSR MURI grants: "Mathematical Infrastructure for Robust Virtual Engineering" and "Unified Theory for Complex Biological and Engineering Networks."
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Record Number:CaltechAUTHORS:20190306-081135649
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Official Citation:K. M. Bobba, B. Bamieh and J. C. Doyle, "Highly optimized transitions to turbulence," Proceedings of the 41st IEEE Conference on Decision and Control, 2002., Las Vegas, NV, USA, 2002, pp. 4559-4562 vol.4. doi: 10.1109/CDC.2002.1185094
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93566
Deposited By: Tony Diaz
Deposited On:06 Mar 2019 16:20
Last Modified:16 Nov 2021 16:59

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