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Analysis and modeling of localized invariant solutions in pipe flow

Paul Ritter1,2, Stefan Zammert3, Baofang Song4,1, Bruno Eckhardt5,6, and Marc Avila1,2,*

  • 1Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, 28359 Bremen, Germany
  • 2Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
  • 3Laboratory for Aero- and Hydrodynamics, TU Delft, 2682 Delft, Netherlands
  • 4Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
  • 5Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany
  • 6JM Burgerscentrum, TU Delft, 2682 Delft, Netherlands

  • *Corresponding author: marc.avila@zarm.uni-bremen.de
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Phys. Rev. Fluids 3, 013901 – Published 5 January, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.013901

Abstract

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds numbers between 1500 and 5000. We compute spatially localized relative periodic orbits in long pipes and show that their upstream and downstream fronts decay exponentially towards the laminar profile. This allows us to model the fronts by employing the linearized Navier-Stokes equations, and the resulting model yields the spatial decay rate and the front velocity profiles of the periodic orbits as a function of Reynolds number, azimuthal wave number, and propagation speed. In addition, when applied to a localized turbulent puff, the model is shown to accurately approximate the spatial decay rate of its upstream and downstream tails. Our study provides insight into the relationship between the kinematics and spatial structure of localized turbulence and more generally into the physics of localization.

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Phys. Rev. Fluids 3, 013901– Published 5 January, 2018
  • Received 31 March 2017
Article part of CHORUS
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