NDLI: Modeling and control of minimal flow unit turbulence in plane Couette flow

Content Provider	IEEE Xplore Digital Library
Author	Smith, T.R. Moehlis, J. Holmes, P.J.
Copyright Year	2003
Description	Author affiliation: Dept. of Mech. & Aerosp. Eng., Princeton Univ., NJ, USA (Smith, T.R.)
Abstract	We model turbulent plane Couette flow for a minimal flow unit (the smallest domain in which turbulence can be sustained) by expanding the velocity field as a sum of optimal modes calculated via the proper orthogonal decomposition from numerical data. Ordinary differential equations are obtained by Galerkin projection of the Navier-Stokes equations onto these modes. We consider a 6 mode (11-dimensional) model. When losses to neglected modes are ignored, the model captures some aspects of the turbulent state very well, but fails to accurately reproduce the velocity field dynamics. However, when energy-transfer to neglected modes is included, there is strong agreement with results from direct numerical simulations. This model provides empirical evidence that the "backbone" for minimal flow unit turbulence is a periodic orbit. We then calculate the phase response curve for this periodic orbit, which describes the phase-shift of the oscillation as a function of the phase of an impulsive perturbation to the mean flow. We see that, depending on its timing, such a perturbation can either advance or retard the time at which subsequent streak breakdowns occur. This suggests how streak breakdown can be controlled through appropriately timed perturbations.
Sponsorship	Honeywell Lab. Xerox Nat. Instruments Math Works
Starting Page	2322
Ending Page	2327
File Size	415622
Page Count	6
File Format	PDF
ISBN	0780379241
ISSN	01912216
DOI	10.1109/CDC.2003.1272965
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-12-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Aerospace engineering Mathematics Cities and towns Differential equations Numerical simulation USA Councils Mathematical model Navier-Stokes equations Aerodynamics Orbital calculations
Content Type	Text
Resource Type	Article

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