Fully localised nonlinear energy growth optimals in pipe flow

Chris C.T. Pringle; A.P. Willis; R.R. Kerswell

doi:10.1063/1.4922183

Fully localised nonlinear energy growth optimals in pipe flow

Chris C.T. Pringle, A.P. Willis, R.R. Kerswell

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Abstract

A new, fully localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal [P. J. Schmid and D. S. Henningson, “Optimal energy density growth in Hagen-Poiseuille flow,” J. Fluid Mech. 277, 192–225 (1994)] is selected and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes [Pringle et al., “Minimal seeds for shear flow turbulence: Using nonlinear transient growth to touch the edge of chaos,” J. Fluid Mech. 702, 415–443 (2012)], but now with full localisation in the streamwise direction. This fully localised optimal perturbation represents the best approximation yet of the minimal seed (the smallest perturbation which is arbitrarily close to states capable of triggering a turbulent episode) for “real” (laboratory) pipe flows. Dependence of the optimal with respect to several parameters has been computed and establishes that the structure is robust.

Original language	English
Article number	064102
Journal	Physics of Fluids
Volume	27
Issue number	6
DOIs	https://doi.org/10.1063/1.4922183
Publication status	Published - 5 Jun 2015

Bibliographical note

Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Pringle, C. , Willis, A.P. and Kerswell, R.R. (2015) Fully localised nonlinear energy growth optimals in pipe flow. Physics of Fluids, volume 27 (6): Article number 064102
and may be found at http://scitation.aip.org/content/aip/journal/pof2/27/6/10.1063/1.4922183.

Keywords

Pipe flow
Best approximations
Critical energy
Hagen-Poiseuille flow
Nonlinear versions
Optimal perturbation
Shear-flow turbulence
Streamwise directions
Transient growth

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Chris Pringle
- Research Centre for Fluid and Complex Systems - Associate Professor Research
Person: Teaching and Research

Cite this

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title = "Fully localised nonlinear energy growth optimals in pipe flow",

abstract = "A new, fully localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal [P. J. Schmid and D. S. Henningson, “Optimal energy density growth in Hagen-Poiseuille flow,” J. Fluid Mech. 277, 192–225 (1994)] is selected and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes [Pringle et al., “Minimal seeds for shear flow turbulence: Using nonlinear transient growth to touch the edge of chaos,” J. Fluid Mech. 702, 415–443 (2012)], but now with full localisation in the streamwise direction. This fully localised optimal perturbation represents the best approximation yet of the minimal seed (the smallest perturbation which is arbitrarily close to states capable of triggering a turbulent episode) for “real” (laboratory) pipe flows. Dependence of the optimal with respect to several parameters has been computed and establishes that the structure is robust. ",

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author = "Pringle, {Chris C.T.} and A.P. Willis and R.R. Kerswell",

note = "Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Pringle, C. , Willis, A.P. and Kerswell, R.R. (2015) Fully localised nonlinear energy growth optimals in pipe flow. Physics of Fluids, volume 27 (6): Article number 064102 and may be found at http://scitation.aip.org/content/aip/journal/pof2/27/6/10.1063/1.4922183.",

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AB - A new, fully localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known (streamwise-independent) linear optimal [P. J. Schmid and D. S. Henningson, “Optimal energy density growth in Hagen-Poiseuille flow,” J. Fluid Mech. 277, 192–225 (1994)] is selected and appears to remain the optimal up until the critical energy at which transition is triggered. The form of this optimal is similar to that found in short pipes [Pringle et al., “Minimal seeds for shear flow turbulence: Using nonlinear transient growth to touch the edge of chaos,” J. Fluid Mech. 702, 415–443 (2012)], but now with full localisation in the streamwise direction. This fully localised optimal perturbation represents the best approximation yet of the minimal seed (the smallest perturbation which is arbitrarily close to states capable of triggering a turbulent episode) for “real” (laboratory) pipe flows. Dependence of the optimal with respect to several parameters has been computed and establishes that the structure is robust.

KW - Pipe flow

KW - Best approximations

KW - Critical energy

KW - Hagen-Poiseuille flow

KW - Nonlinear versions

KW - Optimal perturbation

KW - Shear-flow turbulence

KW - Streamwise directions

KW - Transient growth

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SN - 1089-7666

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JO - Physics of Fluids

JF - Physics of Fluids

IS - 6

M1 - 064102

ER -

Fully localised nonlinear energy growth optimals in pipe flow

Abstract

Bibliographical note

Keywords

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