Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow
Afendikov, Andrei L. and Bridges, Thomas J. (2001) Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow Proceedings of the Royal Society of London A, 457. pp. 257-272.
The linear stability problem for the Hocking-Stewartson pulse, obtained by linearizing the complex Ginzburg-Landau (cGL) equation, is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to stability exponents. A numerical algorithm based on the compound matrix method is developed for computing the Evans function. Using values in the cGL equation associated with spanwise modulation of plane Poiseuille flow, we show that the Hocking-Stewartson pulse associated with points along the neutral curve is always linearly unstable due to a real positive eigenvalue. Implications for the spanwise structure of nonlinear Poiseuille problem between parallel plates are also discussed.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||8 February 2001|
|Uncontrolled Keywords :||Travelling Wave, Evans Function, Hydrodynamic Stability, Compound Matrices|
|Additional Information :||Published in Proceedings of the Royal Society of London A, 457, 257-272. © 2001 The Royal Society.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:40|
|Last Modified :||23 Sep 2013 18:32|
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