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Complexity of the laminar-turbulent boundary in pipe flow

Nazmi Burak Budanur1,2,* and Björn Hof1

  • 1Nonlinear Dynamics and Turbulence Group, IST Austria, 3400 Klosterneuburg, Austria
  • 2Kavli Institute for Theoretical Physics, UC Santa Barbara, Santa Barbara, California 93106, USA

  • *Corresponding author: burak.budanur@ist.ac.at
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Phys. Rev. Fluids 3, 054401 – Published 30 May, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.054401

Abstract

Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry reduction, which we formulate here for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling-wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.

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Phys. Rev. Fluids 3, 054401– Published 30 May, 2018
  • Received 14 February 2018
Article part of CHORUS
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