Fully localised nonlinear energy growth optimals in pipe flow

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

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    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 languageEnglish
    Article number064102
    JournalPhysics of Fluids
    Issue number6
    Publication statusPublished - 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.


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


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