Visualizing the geometry of state space in plane Couette flow
TLDR
In this article, a dynamical 10 5-dimensional state-space representation of plane Couette flow at Reynolds number Re = 400 in a small periodic cell is presented, which partially tessellates the region of state space explored by transiently turbulent dynamics with a rigid web of symmetry-induced heteroclinic connections.Abstract:
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 10 5 -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.read more
Citations
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The Significance of Simple Invariant Solutions in Turbulent Flows
TL;DR: In this paper, the authors describe some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows.
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The Significance of Simple Invariant Solutions in Turbulent Flows
TL;DR: In this article, the authors describe some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows.
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Equilibrium and travelling-wave solutions of plane Couette flow
TL;DR: In this paper, the authors presented 10 equilibrium solutions to plane Couette flow in small periodic cells at low Reynolds number Re and two new travelling-wave solutions, which are continued under changes of Re and spanwise period.
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Statistical structure of self-sustaining attached eddies in turbulent channel flow
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Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow
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