Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q01: Nonlinear Dynamics: Model Reduction II
12:50 PM–3:26 PM,
Tuesday, November 20, 2018
Georgia World Congress Center
Room: B201
Chair: Pedram Hassenzadeh, Rice University
Abstract ID: BAPS.2018.DFD.Q01.6
Abstract: Q01.00006 : Koopman mode expansions between two invariant sets*
1:55 PM–2:08 PM
Presenter:
Rich Kerswell
(Univ of Cambridge)
Authors:
Jacob Page
(Univ of Cambridge)
Rich Kerswell
(Univ of Cambridge)
Koopman mode expansions have been touted as a very useful way to represent nonlinear dynamics given the ability of dynamic mode decomposition to extract the modes from data. Here we explore how such an approach works for heteroclinic dynamics between two equilibria using a 1D nonlinear system (a pitchfork bifurcation) which allows explicit calculations. Well-defined Koopman mode expansions are found to exist around either equilibria but each fails at the same intermediary point between them indicating that there is no uniformly valid Koopman expansion for the dynamics. Results will be presented to indicate that this lack of uniformity carries over to the 3D Navier-Stokes equations as well.
*This work is supported by EPSRC (UK) which is gratefully acknowledged.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2018.DFD.Q01.6
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