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Speaker : Troy Smoth
Control & Dynamical Systems, Caltech
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Title:
LOW DIMENSIONAL MODELS OF PLANE COUETTE FLOW
USING THE PROPER ORTHOGONAL DECOMPOSITION
Abstract:
This talk describes efforts to model plane Couette flow in a minimal flow
unit -- a domain whose spanwise and streamwise extent is just sufficient
to maintain turbulence -- by expanding the velocity field as a sum of
optimal modes calculated via proper orthogonal decomposition from
numerical data. Ordinary differential equations are obtained by Galerkin
projection of the Navier-Stokes equations onto these modes. The focus
will be on two models consisting of only a few ordinary differential
equations, the dynamics of which convincingly approximate the dynamics of
plane Couette flow. The "core" of these models is the quadratic normal
form describing the generic interaction of Fourier modes of wavenumbers 0,
1 and 2 under the symmetry group O(2) of rotations and reflections.
Several types of interesting dynamics for this system, which is a
generalisation of the 1:2 modal interaction studied by Armbruster,
Guckenheimer, Holmes and others, will also be discussed.
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