Forecasting Fluid Flows Using the Geometry of Turbulence

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

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


The existence and dynamical role of particular unstable solutions (exact coherent structures) of the Navier-Stokes equation is revealed in laboratory studies of weak turbulence in a thin, electromagnetically driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.

Original languageEnglish (US)
Article number114501
JournalPhysical review letters
Issue number11
StatePublished - Mar 15 2017
Externally publishedYes

Bibliographical note

Funding Information:
This work is supported by the National Science Foundation under Grants No.CMMI-1234436 and No.DMS-1125302.

Publisher Copyright:
© 2017 American Physical Society.


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