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

Balachandra Suri, Jeffrey Tithof, Roman O. Grigoriev, Michael F. Schatz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Article number023105
JournalPhysical Review E
Volume98
Issue number2
DOIs
StatePublished - Aug 13 2018
Externally publishedYes

Bibliographical note

Funding Information:
This work is supported by grants from the National Science Foundation (Grants No. CMMI-1234436, No. DMS-1125302, and No. CMMI-1725587) and Defense Advanced Research Projects Agency (Grant No. HR0011-16-2-0033).

Funding Information:
This work is supported by grants from the National Science Foundation (Grants No. CMMI-1234436, No. DMS-1125302, and No. CMMI-1725587) and Defense Advanced Research Projects Agency (Grant No. HR0011-16-2-0033).

Publisher Copyright:
© 2018 American Physical Society.

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