Modeling Transition: New Scenarios, System Sensitivity and Feedback Control


The problem of controlling or delaying transition to turbulence in shear flows has been the subject of numerous papers over the past twenty years. Although there is no single matmatical framework that describes transition for all possible flows, new approaches to (non-classical) linear hydrodynamic stability theory have provided tremendous improvements in the fundamental understanding of this process. in particular, ideas from robust control theory have been used to develop new linear theories in an attempt to explain some of the failures of classical linear hydrodynamic stability theory. This may be exploited in control design and analysis. in addition, these theories have been tested on low-dimensional model problems with mixed success. in this paper, we review some of these linear thories and discuss to roles of uncertainty, system sensitivity and modern feedback control in the transition problem. a boundary control problem defined by Burgers' equation is employed to illustrate how the distributed parameter control theory can be used as a framework for computing feedback functional gains that provide practical guidance in sensor/actuator placement. Low-dimensional models are employed to explain the basic idea and to illustrate how one cam employ bifurcation analysis to predict transition. Thes examples are also used to show how feedback controllers can delay transition and alter the global dynamics of such systems.


Mathematics and Statistics

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Book - Chapter

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© 2005 World Scientific Publishing Company, All rights reserved.

Publication Date

01 Jan 2005