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Basis for finding exact coherent states

Ahmed, M. Arslan and Sharma, Ati S. (2020) Basis for finding exact coherent states. Physical Review E, 101 (1). Art. No. 012213. ISSN 2470-0045. doi:10.1103/physreve.101.012213.

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One of the outstanding problems in the dynamical systems approach to turbulence is to find a sufficient number of invariant solutions to characterize the underlying dynamics of turbulence [Annu. Rev. Fluid Mech. 44, 203 (2012)]. As a practical matter, the solutions can be difficult to find. To improve this situation, we show how to find periodic orbits and equilibria in plane Couette flow by projecting pseudorecurrent segments of turbulent trajectories onto the left-singular vectors of the Navier-Stokes equations linearized about the relevant mean flow (resolvent modes). The projections are, subsequently, used to initiate Newton-Krylov-hookstep searches, and new (relative) periodic orbits and equilibria are discovered. We call the process project-then-search and validate the process by first applying it to previously known fixed point and periodic solutions. Along the way, we find new branches of equilibria, which include bifurcations from previously known branches, and new periodic orbits that closely shadow turbulent trajectories in state space.

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Ahmed, M. Arslan0000-0002-3479-6946
Sharma, Ati S.0000-0002-7170-1627
Additional Information:© 2020 American Physical Society. Received 12 July 2019; revised manuscript received 2 January 2020; published 24 January 2020. This paper has been supported by the Air Force Office of Scientific Research (European Office of Aerospace Research and Development) under Award No. FA9550-14-1-0042. We would like to thank Professor J. Gibson for providing his code, equilibrium solutions, and helpful comments. We would also like to acknowledge Professor E. Knobloch for his guidance and Dr. D. Lasagna for his probing questions and useful recommendations. This work was completed, in part, at the Kavli Institute for Theoretical Physics with support from the National Science Foundation under Grant No. NSF PHY11-25915.
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Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0042
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Record Number:CaltechAUTHORS:20200124-130816542
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100900
Deposited By: Tony Diaz
Deposited On:25 Jan 2020 03:36
Last Modified:16 Nov 2021 17:57

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