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The theory of stability of spatially periodic parallel flows

Published online by Cambridge University Press:  20 April 2006

Kanefusa Gotoh ,
Michio Yamada  and
Jiro Mizushima
Kanefusa Gotoh
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, Japan
Michio Yamada
Affiliation:
Department of Physics, Faculty of Science, Kyoto University, Kyoto 606, Japan
Jiro Mizushima
Affiliation:
Department of Information Science, Sagami Institute of Technology, Fujisawa 251, Japan
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Abstract

The stability of a parallel flow periodic in the direction normal to the stream is investigated theoretically. Critical Reynolds numbers are calculated for a general velocity profile including widely separated wakes. The critical mode of disturbance is found to have the same period as the basic flow. Growing modes with much larger periods exist, however, at slightly supercritical values of the Reynolds number. The analysis of various limiting cases explains the qualitative difference in the shape of the neutral curves depending on the period of the disturbance. In connection with the results obtained in this paper, the stability of non-parallel periodic flows is briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 45 - 58
Copyright
© 1983 Cambridge University Press

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