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A traveling wave bifurcation analysis of turbulent pipe flow

Engel, Maximilian ; Kuehn, Christian; de Rijk, Björn 1
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)

Abstract:

Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al 2015 Nature 526 550–3], which describes the rise of turbulent pipe flow via a PDE system of reduced complexity. The fast evolution of turbulence is governed by reaction-diffusion dynamics coupled to the centerline velocity, which evolves with advection of Burgers' type and a slow relaminarization term. Applying to this model a spatial dynamics ansatz and geometric singular perturbation theory, we prove the existence of a heteroclinic loop between a turbulent and a laminar steady state and establish a cascade of bifurcations of various traveling waves mediating the transition to turbulence. The most complicated behaviour can be found in an intermediate Reynolds number regime, where the traveling waves exhibit arbitrarily long periodic-like dynamics indicating the onset of chaos. Our analysis provides a systematic mathematical approach to identifying the transition to spatio–temporal turbulent structures that may also be applicable to other models arising in fluid dynamics.


Verlagsausgabe §
DOI: 10.5445/IR/1000152025
Veröffentlicht am 27.10.2022
Originalveröffentlichung
DOI: 10.1088/1361-6544/ac9504
Scopus
Zitationen: 1
Web of Science
Zitationen: 1
Dimensions
Zitationen: 1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 0951-7715, 1361-6544
KITopen-ID: 1000152025
Erschienen in Nonlinearity
Verlag Institute of Physics Publishing Ltd (IOP Publishing Ltd)
Band 35
Heft 11
Seiten 5903–5937
Vorab online veröffentlicht am 13.10.2022
Schlagwörter bifurcations, heteroclinic loop, pipe flow, reaction–diffusion–advection system, traveling waves, turbulence, geometric singular perturbation theory
Nachgewiesen in Scopus
Web of Science
Dimensions
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