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...
Main Author: | |
---|---|
Other Authors: | |
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/ |
id |
ndltd-VTETD-oai-vtechworks.lib.vt.edu-10919-28051 |
---|---|
record_format |
oai_dc |
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 |
_version_ |
1719341217927397376 |