Title: |
A Robust Control Approach to Understanding Nonlinear Mechanisms in Shear Flow Turbulence |
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Speaker: |
Dr. Dennice Gayme |
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Affiliation: |
California Institute of Technology, Pasadena, Ca |
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When: |
Thursday, October 28, 2010 at 11:00:00 AM |
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Where: |
Love Building, Room 185 |
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Host: |
Andrea Para | |
Abstract It is well known that the laminar profile in plane Couette flow is linear while the turbulent velocity profile is a blunted S shape. On the other hand, the underlying mechanisms involved in creating this blunted profile still remain unknown. Previous work shows that linear models generate flows with streamwise elongated features reminiscent of those observed through experiments. However, a nonlinear model is required to capture the momentum transfer that produces a turbulent velocity profile. Numerical and experimental observations which suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures motivate the study of a streamwise constant projection of the Navier Stokes equations. The resulting two-dimensional, three velocity component (2D/3C) nonlinear model captures important nonlinear features of turbulence, while maintaining the linear mechanisms that have been shown to be necessary to maintain turbulence. In this talk, I describe how this 2D/3C model in a robust control framework can be used to rigorously connect experimental observations of streamwise coherence to the shape of the mean velocity profile. Small amplitude Gaussian noise forcing is applied to simulate the model's response in the presence of disturbances, uncertainty and modeling errors. A comparison of the simulation results to experimentally verified DNS data demonstrates that this system model captures salient features of fully developed turbulence, particularly the change in mean velocity profile. A forced version of the 2D/3C model shows that the momentum transfer that produces a urbulent-like mean profile requires a nonlinear streamwise velocity equation. Finally, I attempt to make a connection between the linear processes responsible for large disturbance amplification and the nonlinearity required for the blunting. I show that while the linear equations allow one to appropriately model the spanwise extent of the large-scale streamwise structures, this comes at the expense of capturing the mean velocity profile. |
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Biography Dennice Gayme is a postdoctoral scholar in the Computing and Mathematical Sciences Department at the California Institute of Technology. She received her doctorate in Control and Dynamical Systems in 2010 under the supervision of John C. Doyle and Beverley J. McKeon, also at the California Institute of Technology where she was a recipient of the P.E.O. scholar award in 2007 and the James Irvine Foundation Graduate Fellowship in 2003. She received a Masters of Science in Mechanical Engineering from the University of California at Berkeley in 1998. Prior to her doctorial work she was a Senior Research Scientist in the Systems and Control Technology and Vehicle Health Monitoring Groups at Honeywell Laboratories from 1999-2003. Dennice's research interests are in the study of large-scale interconnected systems in the broad area of energy with applications focused in the areas of control theoretic analysis of shear flow turbulence and the integration of renewable power sources into a smart electric power system. |
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