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Wave packets, resonant interactions and soliton formation in inlet pipe flow

Published online by Cambridge University Press:  26 April 2006

Igor V. Savenkov
Igor V. Savenkov
Affiliation:
Computer Center of the Academy of Sciences, 117 967 Vavilova, 40, Moscow, Russia, CIS
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Abstract

The development of disturbances (two-dimensional non-linear and three-dimensional linear) in the entrance region of a circular pipe is studied in the limit of Reynolds number R → ∞ in the framework of triple-deck theory. It is found that lower-branch axisymmetric disturbances can interact in the resonant manner. Numerical calculations show that a two-dimensional nonlinear wave packet grows much more rapidly than that in the boundary layer on a flat plate, producing a spike-like solution which seems to become singular at a finite time. Large-sized, short-scaled disturbances are also studied. In this case the development of axisymmetric disturbances is governed by single one-dimensional equation in the form of the Korteweg-de Vries and Benjamin-Ono equations in the long- and short-wave limits respectively. The nonlinear interactions of these disturbances lead to the formation of solitons which can run both upstream and downstream. Linear three-dimensional wave packets are also calculated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 1 - 30
Copyright
© 1993 Cambridge University Press

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