Visualizing the geometry of state space in plane Couette flow
By J. Gibson, Jonathan J. Halcrow, Predrag Cvitanović. Journal of Fluid Mechanics, 2007
344 citations recorded by the source corpus.
Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier–Stokes equations. We construct a dynamical 105-dimensional state-space representation of plane Couette flow at Reynolds number Re = 400 in a small periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute a new equilibrium solution of plane Couette flow and the leading eigenvalues and eigenfunctions of known equilibria at this Re and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly elegant dynamical-systems visualization of moderate-Re turbulence. The invariant manifolds partially tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of symmetry-induced heteroclinic connections.
Subfields: Computational Mechanics, Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0aedcc9f573bf65264472696a778d4e25e6d833a
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Citations in the corpus
- Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number (2010, background): “the ones of Gustavsson (1991) and Butler & Farrell (1992) for the optimal temporal response, Trefethen et al.”
- The Significance of Simple Invariant Solutions in Turbulent Flows (2011, methodology): “Other equilibrium solutions have been found more recently for Couette flow (Gibson et al. 2008, 2009, Itano & Generalis 2009, Nagata 1997, Schmiegel 1999). They are not necessarily related to the one originally identified by Nagata (1990), but they have been used to discuss coherent structures or th”