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The Quarterly Journal of Mechanics and Applied Mathematics 1986 39(1):25-40; doi:10.1093/qjmam/39.1.25
© 1986 by Oxford University Press
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NONLINEAR STABILITY BOUNDS FOR PLANE POISEUILLE FLOW SUBJECTED TO UNIPOLAR CHARGE INJECTION

A. T. RICHARDSON and B. J. S. DEO {dagger}

( Department of Engineering Mathematics, University of Bristol )

Generalized energy stability analysis is applied to a plane Poiseuille flow of dielectric liquid subjected to an injection of unipolar space charge. Using both an energy functional and one incorporating space-charge perturbations, sufficient conditions to guarantee global monotonic stability in the mean are derived. In both cases it is found that the most energetic disturbance is a transverse roll, that is, one aligned perpendicularly to the direction of fluid flow.


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