Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow

B. Suri, J. Tithof, R. Grigoriev, M. Schatz, Physical Review E 98 (2018).

Journal Article | Published | English
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Abstract
Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.
Publishing Year
Journal Title
Physical Review E
Volume
98
Issue
2
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Suri B, Tithof J, Grigoriev R, Schatz M. Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E. 2018;98(2). doi:10.1103/PhysRevE.98.023105
Suri, B., Tithof, J., Grigoriev, R., & Schatz, M. (2018). Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E, 98(2). https://doi.org/10.1103/PhysRevE.98.023105
Suri, Balachandra, Jeffrey Tithof, Roman Grigoriev, and Michael Schatz. “Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow.” Physical Review E 98, no. 2 (2018). https://doi.org/10.1103/PhysRevE.98.023105.
B. Suri, J. Tithof, R. Grigoriev, and M. Schatz, “Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow,” Physical Review E, vol. 98, no. 2, 2018.
Suri B, Tithof J, Grigoriev R, Schatz M. 2018. Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow. Physical Review E. 98(2).
Suri, Balachandra, et al. “Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow.” Physical Review E, vol. 98, no. 2, American Physiological Society, 2018, doi:10.1103/PhysRevE.98.023105.

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