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The energy balance in modulated plane Poiseuille flow

Published online by Cambridge University Press:  29 March 2006

D. M. Herbert
D. M. Herbert
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

Plane Poiseuille flow in which the pressure gradient has a small amplitude time-periodic component in addition to a constant component is considered. The velocity field close to the boundaries, arising from a small amplitude high frequency disturbance to the flow, is calculated to second order in the modulation amplitude. The energy-transfer integral for the disturbance is then calculated to the same order. It is found that, if the thickness of the disturbance shear wave relative to that of the modulation shear wave is greater than ½, the modulation inhibits energy transfer into the disturbance and so stabilizes the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 1 , 14 November 1972 , pp. 73 - 80
Copyright
© 1972 Cambridge University Press

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References

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