Transition in pipe flow: the saddle structure on the boundary of turbulence
By Yohann Duguet, Ashley P. Willis, Rich R. Kerswell. Journal of Fluid Mechanics, 2007
162 citations recorded by the source corpus.
The laminar–turbulent boundary Σ is the set separating initial conditions which relaminarize uneventfully from those which become turbulent. Phase space trajectories on this hypersurface in cylindrical pipe flow appear to be chaotic and show recurring evidence of coherent structures. A general numerical technique is developed for recognizing approaches to these structures and then for identifying the exact coherent solutions themselves. Numerical evidence is presented which suggests that trajectories on Σ are organized around only a few travelling waves and their heteroclinic connections. If the flow is suitably constrained to a subspace with a discrete rotational symmetry, it is possible to find locally attracting travelling waves embedded within Σ. Four new types of travelling waves were found using this approach.
Subfields: Computational Mechanics, Computer Networks and Communications, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2f19db7819855961d5532c2a3e268e12685dcd2f
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In Computational Mechanics
- Rich R. Kerswell
- Matthew P. Juniper
- Dwight Barkley
- Clarence W. Rowley
- Denis Sipp
- R. Sujith
- Sunil Ahuja
- Spencer J. Sherwin
In Computer Networks and Communications
In Statistical and Nonlinear Physics
Citations in the corpus
- Theoretical perspective on the route to turbulence in a pipe (2016, background): “Edge states are important and much studied in subcritical shear flows (e.g. Itano & Toh 2001; Eckhardt et al. 2007; Duguet et al. 2008; Mellibovsky et al. 2009).”
- Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition (2010, background): “The unstable periodic solution, which sits on the basin boundary, corresponds to the local relative attractor in Duguet et al. (2008) or, equivalently, the steady or quasi-steady periodic state identified in stage 3 of Schmid & Henningson (2001).”
- Nonlinear Nonmodal Stability Theory (2018, background): “This can be unique and simple (e.g. the equilibrium in Schneider et al. 2008) but more generally is non-unique (§3.6 of Duguet et al. 2008) and chaotic (e.g. Schneider et al. 2007, Mellibovsky et al. 2009).”