Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows, this approach has failed to match experimental results. Recently, new scenarios for transition have b...

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Main Author: Singler, John
Other Authors: Mathematics
Format: Others
Published: Virginia Tech 2014
Subjects:
Online Access:http://hdl.handle.net/10919/28051
http://scholar.lib.vt.edu/theses/available/etd-06162005-203749/
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spelling ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-280512020-09-26T05:33:11Z Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow Singler, John Mathematics Burns, John A. Cliff, Eugene M. Borggaard, Jeffrey T. Iliescu, Traian Herdman, Terry L. Sensitivity Analysis Small Disturbances Transition to Turbulence Partial Differential Equations For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows, this approach has failed to match experimental results. Recently, new scenarios for transition have been proposed that are based on the non-normality of the linearized operator. These new â mostly linearâ theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored. The main goal of this work is to begin to study the role of nonlinearity in transition. We use model problems to illustrate that small unmodeled disturbances can cause transition through movement or bifurcation of equilibria. We also demonstrate that small wall roughness can lead to transition by causing the linearized system to become unstable. Sensitivity methods are used to obtain important information about the disturbed problem and to illustrate that it is possible to have a precursor to predict transition. Finally, we apply linear feedback control to the model problems to illustrate the power of feedback to delay transition and even relaminarize fully developed chaotic flows. Ph. D. 2014-03-14T20:13:10Z 2014-03-14T20:13:10Z 2005-06-15 2005-06-16 2005-07-07 2005-07-07 Dissertation etd-06162005-203749 http://hdl.handle.net/10919/28051 http://scholar.lib.vt.edu/theses/available/etd-06162005-203749/ JRS_thesis.pdf In Copyright http://rightsstatements.org/vocab/InC/1.0/ application/pdf Virginia Tech
collection NDLTD
format Others
sources NDLTD
topic Sensitivity Analysis
Small Disturbances
Transition to Turbulence
Partial Differential Equations
spellingShingle Sensitivity Analysis
Small Disturbances
Transition to Turbulence
Partial Differential Equations
Singler, John
Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow
description For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows, this approach has failed to match experimental results. Recently, new scenarios for transition have been proposed that are based on the non-normality of the linearized operator. These new â mostly linearâ theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored. The main goal of this work is to begin to study the role of nonlinearity in transition. We use model problems to illustrate that small unmodeled disturbances can cause transition through movement or bifurcation of equilibria. We also demonstrate that small wall roughness can lead to transition by causing the linearized system to become unstable. Sensitivity methods are used to obtain important information about the disturbed problem and to illustrate that it is possible to have a precursor to predict transition. Finally, we apply linear feedback control to the model problems to illustrate the power of feedback to delay transition and even relaminarize fully developed chaotic flows. === Ph. D.
author2 Mathematics
author_facet Mathematics
Singler, John
author Singler, John
author_sort Singler, John
title Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow
title_short Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow
title_full Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow
title_fullStr Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow
title_full_unstemmed Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow
title_sort sensitivity analysis of partial differential equations with applications to fluid flow
publisher Virginia Tech
publishDate 2014
url http://hdl.handle.net/10919/28051
http://scholar.lib.vt.edu/theses/available/etd-06162005-203749/
work_keys_str_mv AT singlerjohn sensitivityanalysisofpartialdifferentialequationswithapplicationstofluidflow
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