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A periodic-like solution in channel flow

Published online by Cambridge University Press:  28 April 2003

SADAYOSHI TOH  and
TOMOAKI ITANO
SADAYOSHI TOH
Affiliation:
Department of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
TOMOAKI ITANO
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
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Abstract

We search channel flow for unsteady solutions for different Reynolds numbers and configurations by extending a shooting method which was previously used to obtain a travelling-wave solution. A general initial condition is considered. A periodic-like solution to the incompressible Navier–Stokes equations in a minimal flow unit is found. One cycle of the solution consists of two typical intervals: a single-streak period and a double-streak period. The solution seems to be periodic; however, it cannot be distinguished from a heteroclinic cycle which consists of two heteroclinic orbits connecting two single-streak solutions, because the solution is tracked only for one and half periods.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 481 , 25 April 2003 , pp. 67 - 76
Copyright
© 2003 Cambridge University Press

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