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Title: Parameterization of travelling waves in plane Poiseuille flow
Authors: Smith, WR
Wissink, JG
Keywords: Maximum-entropy configurations;Parameterization;Plane Poiseuille flow
Issue Date: 2014
Publisher: Oxford University Press
Citation: IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 2014, 79 (1), pp. 22 - 32
Abstract: The first finite-dimensional parameterization of a subset of the phase space of the Navier-Stokes equations is presented. Travelling waves in two-dimensional plane Poiseuille flow are numerically shown to approximate maximum-entropy configurations. In a coordinate system moving with the phase velocity, the enclosed body of the flow exhibits a hyperbolic sinusoidal relationship between the vorticity and stream function. The phase velocity and two-amplitude parameters describe the stable manifold on the slow viscous time scale. This original parameterization provides a valuable visualization of this subset of the phase space of the Navier-Stokes equations. These new results provide physical insight into an important intermediate stage in the instability process of plane Poiseuille flow.
Description: © The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copyedited, author-produced PDF of an article accepted for publication in [IMA Journal of Applied Mathematics ] following peer review. The version of record [ IMA Journal of Applied Mathematics (2014) 79(1): 22-32.] is available online at:
ISSN: 0272-4960
Appears in Collections:Dept of Mechanical Aerospace and Civil Engineering Research Papers

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