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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: http://imamat.oxfordjournals.org/content/79/1/22 |
URI: | http://imamat.oxfordjournals.org/content/79/1/22 http://bura.brunel.ac.uk/handle/2438/9882 |
DOI: | http://dx.doi.org/10.1093/imamat/hxs037 |
ISSN: | 0272-4960 1464-3634 |
Appears in Collections: | Dept of Mechanical and Aerospace Engineering Research Papers |
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