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Title: Fully localised nonlinear energy growth optimals in pipe flow

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.
Authors:
 [1] ;  [2] ;  [3]
  1. Applied Mathematics Research Centre, Department of Mathematics and Physics, Coventry University, Coventry (United Kingdom)
  2. School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH (United Kingdom)
  3. Department of Mathematics, University of Bristol, Bristol BS8 1TW (United Kingdom)
Publication Date:
OSTI Identifier:
22403235
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CHAOS THEORY; DISTURBANCES; ENERGY DENSITY; FLOW RATE; LAMINAR FLOW; MASS TRANSFER; NONLINEAR PROBLEMS; PIPES; SHEAR; TURBULENCE