A streamwiseconstant model of turbulent pipe flow
A streamwiseconstant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. The model is subject to two different types of forcing: a simple forcing of the axial momentum equation via a deterministic form for the streamfu...
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American Institute of Physics
2011

Online Access:  https://authors.library.caltech.edu/27781/1/Bourguignon2011p16218Phys_Fluids.pdf http://resolver.caltech.edu/CaltechAUTHORS:20111115094643184 https://authors.library.caltech.edu/27781/ 
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educaltechauthors2778120160921T22:21:14Z A streamwiseconstant model of turbulent pipe flow Bourguignon, JeanLoup McKeon, Beverley J. A streamwiseconstant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. The model is subject to two different types of forcing: a simple forcing of the axial momentum equation via a deterministic form for the streamfunction and a stochastic forcing of the streamfunction equation. Using a single forced momentum balance equation, we show that the shape of the velocity profile is robust to changes in the forcing profile and that both linear nonnormal and nonlinear effects are required to capture the change in mean flow associated with transition to turbulence. The particularly simple form of the model allows for the study of the momentum transfer directly by inspection of the equations. The distribution of the high and lowspeed streaks over the crosssection of the pipe produced by our model is remarkably similar to one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition. Under stochastic forcing, the model exhibits a quasiperiodic selfsustaining cycle characterized by the creation and subsequent decay of “streamwiseconstant puffs,” socalled due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with threedimensional puffs in a frame of reference moving at the bulk velocity. We establish that the flow dynamics are relatively insensitive to the regeneration mechanisms invoked to produce nearwall streamwise vortices, such that using small, unstructured background disturbances to regenerate the streamwise vortices in place of the natural feedback from the flow is sufficient to capture the formation of the high and lowspeed streaks and their segregation leading to the blunting of the velocity profile characteristic of turbulent pipe flow. We propose a “quasi selfsustaining process” to describe these mechanisms. American Institute of Physics 201109 Article PeerReviewed application/pdf https://authors.library.caltech.edu/27781/1/Bourguignon2011p16218Phys_Fluids.pdf http://resolver.caltech.edu/CaltechAUTHORS:20111115094643184 Bourguignon, JeanLoup and McKeon, Beverley J. (2011) A streamwiseconstant model of turbulent pipe flow. Physics of Fluids, 23 (9). 095111. ISSN 10706631. http://resolver.caltech.edu/CaltechAUTHORS:20111115094643184 <http://resolver.caltech.edu/CaltechAUTHORS:20111115094643184> https://authors.library.caltech.edu/27781/ 
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A streamwiseconstant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. The model is subject to two different types of forcing: a simple forcing of the axial momentum equation via a deterministic form for the streamfunction and a stochastic forcing of the streamfunction equation. Using a single forced momentum balance equation, we show that the shape of the velocity profile is robust to changes in the forcing profile and that both linear nonnormal and nonlinear effects are required to capture the change in mean flow associated with transition to turbulence. The particularly simple form of the model allows for the study of the momentum transfer directly by inspection of the equations. The distribution of the high and lowspeed streaks over the crosssection of the pipe produced by our model is remarkably similar to one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition. Under stochastic forcing, the model exhibits a quasiperiodic selfsustaining cycle characterized by the creation and subsequent decay of “streamwiseconstant puffs,” socalled due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with threedimensional puffs in a frame of reference moving at the bulk velocity. We establish that the flow dynamics are relatively insensitive to the regeneration mechanisms invoked to produce nearwall streamwise vortices, such that using small, unstructured background disturbances to regenerate the streamwise vortices in place of the natural feedback from the flow is sufficient to capture the formation of the high and lowspeed streaks and their segregation leading to the blunting of the velocity profile characteristic of turbulent pipe flow. We propose a “quasi selfsustaining process” to describe these mechanisms. 
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Article 
author 
Bourguignon, JeanLoup McKeon, Beverley J. 
spellingShingle 
Bourguignon, JeanLoup McKeon, Beverley J. A streamwiseconstant model of turbulent pipe flow 
author_facet 
Bourguignon, JeanLoup McKeon, Beverley J. 
author_sort 
Bourguignon, JeanLoup 
title 
A streamwiseconstant model of turbulent pipe flow 
title_short 
A streamwiseconstant model of turbulent pipe flow 
title_full 
A streamwiseconstant model of turbulent pipe flow 
title_fullStr 
A streamwiseconstant model of turbulent pipe flow 
title_full_unstemmed 
A streamwiseconstant model of turbulent pipe flow 
title_sort 
streamwiseconstant model of turbulent pipe flow 
publisher 
American Institute of Physics 
publishDate 
2011 
url 
https://authors.library.caltech.edu/27781/1/Bourguignon2011p16218Phys_Fluids.pdf http://resolver.caltech.edu/CaltechAUTHORS:20111115094643184 https://authors.library.caltech.edu/27781/ 
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