The problem of controlling or delaying transition to turbulence in shear flows has been the subject of numerous papers over the past twenty years. This period has seen the development of several low dimensional models for parallel shear flows in an attempt to explain the failure of classical linear hydrodynamic stability theory to correctly predict transition. In recent years, ideas from robust control theory have been employed to attack this problem. In this paper we use these models to develop a scenario for transition that employs both classical bifurcation theory and robust control theory. In addition, we present numerical results to illustrate the ideas and to show how feedback can be used to delay transition. We close with a specific conjecture and discuss some previous results along this line.
J. A. Burns and J. R. Singler, "Feedback Control of Low Dimensional Models of Transition to Turbulence," Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, 2005, Institute of Electrical and Electronics Engineers (IEEE), Jan 2006.
The definitive version is available at https://doi.org/10.1109/CDC.2005.1582644
44th IEEE Conference on Decision and Control, and the European Control Conference, 2005
Mathematics and Statistics
United States. Air Force. Office of Scientific Research
Keywords and Phrases
Shear Flows; Transition; Turbulence
Article - Conference proceedings
© 2006 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.