Multiscale model reduction for incompressible flows
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Published:2023-10-11
Issue:
Volume:973
Page:
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ISSN:0022-1120
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Container-title:Journal of Fluid Mechanics
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language:en
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Short-container-title:J. Fluid Mech.
Author:
Callaham Jared L.ORCID,
Loiseau Jean-ChristopheORCID,
Brunton Steven L.ORCID
Abstract
We introduce a projection-based model reduction method that systematically accounts for nonlinear interactions between the resolved and unresolved scales of the flow in a low-dimensional dynamical systems model. The proposed method uses a separation of time scales between the resolved and subscale variables to derive a reduced-order model with cubic closure terms for the truncated modes, generalizing the classic Stuart–Landau equation. The leading-order cubic terms are determined by averaging out fast variables through a perturbation series approximation of the action of a stochastic Koopman operator. We show analytically that this multiscale closure model can capture both the effects of mean-flow deformation and the energy cascade before demonstrating improved stability and accuracy in models of chaotic lid-driven cavity flow and vortex pairing in a mixing layer. This approach to closure modelling establishes a general theory for the origin and role of cubic nonlinearities in low-dimensional models of incompressible flows.
Funder
Army Research Office
U.S. Department of Defense
National Science Foundation
Air Force Office of Scientific Research
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics