Citation
Maynard Gayme, Dennice (2010) A robust control approach to understanding nonlinear mechanisms in shear flow turbulence. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05272010195149679
Abstract
A robust control framework is used to investigate a streamwise constant projection of the Navier Stokes equations for plane Couette flow. Study of this streamwise constant model is motivated by both numerical and experimental observations that suggest the prevalence and importance of streamwise and quasistreamwise elongated structures. Smallamplitude Gaussian noise forcing is applied to a twodimensional, threevelocity component (2D/3C) model to describe its response in the presence of disturbances, uncertainty and modeling errors. A comparison of the results with Direct Numerical Simulation (DNS) data demonstrates that the simulations capture salient features of fully developed turbulence. In particular, the change in mean velocity profile from the nominal laminar to the characteristic “S” shaped turbulent profile. The application of Taylor’s hypothesis shows that the model can also reproduce downstream information in the form of largescale coherence resembling numerically and experimentally observed flow features. The 2D/3C model is able to generate “turbulentlike” behavior under smallamplitude stochastic noise. The laminar flow solution is globally stable, therefore transition to turbulence in this model is likely a consequence of the laminar flow solution’s lack of robustness in the presence of disturbances and uncertainty. In fact, large disturbance amplification is common in both this model and the linearized Navier Stokes equations. Periodic spanwise/wallnormal (z–y) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity equation. The resulting steadystate solution is qualitatively similar to a fully turbulent spatial field of DNS data. Both numerical methods and a perturbation analysis confirm that the momentum transfer that produces a “turbulentlike” mean profile requires a nonlinear streamwise velocity equation. A system theoretic approach is used to study the amplification mechanisms that develop through the 2D/3C nonlinear coupling in the streamwise velocity equation. The spanwise/wallnormal plane forcing required to produce each stream function is computedand used to define an induced norm from this forcing input to the streamwise velocity. This inputoutput response is used to determine the energy optimal spanwise wavelength (i.e.,the preferential spacing) over a range of Reynolds numbers and forcing amplitudes.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Shear flow turbulence; Coherent structures in Couette flow; Energy amplification; Nonlinear mechanisms in shear flow turbulence; Streamwise constant flow; Transition to turbulence as a robustness problem 
Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Control and Dynamical Systems 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  19 May 2010 
Author Email:  dennice (AT) cds.caltech.edu 
Record Number:  CaltechTHESIS:05272010195149679 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:05272010195149679 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  5871 
Collection:  CaltechTHESIS 
Deposited By:  Dennice Maynard Gayme 
Deposited On:  04 Jun 2010 16:41 
Last Modified:  26 Dec 2012 03:26 
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