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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. https://resolver.caltech.edu/CaltechAUTHORS:20200124-130816542

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physreve.101.012213DOIArticle
ORCID:
AuthorORCID
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.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0042
NSFPHY11-25915
Issue or Number:1
Record Number:CaltechAUTHORS:20200124-130816542
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200124-130816542
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100900
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Jan 2020 03:36
Last Modified:25 Jan 2020 03:36

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