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Forecasting Fluid Flows Using the Geometry of Turbulence

Balachandra Suri, Jeffrey Tithof, Roman O. Grigoriev, and Michael F. Schatz
Phys. Rev. Lett. 118, 114501 – Published 15 March 2017
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Abstract

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.

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  • Received 9 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.114501

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

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Searching for Order in Turbulent Flow

Published 17 March 2017

The observation of ordered flow patterns in a weakly turbulent liquid may lead to new ways of predicting the evolution of turbulent flow.

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Authors & Affiliations

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

  • School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA

  • *michael.schatz@physics.gatech.edu

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Issue

Vol. 118, Iss. 11 — 17 March 2017

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