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Bounds for turbulent shear flow

Published online by Cambridge University Press:  29 March 2006

F. H. Busse
F. H. Busse
Affiliation:
Max-Planck-Institut für Physik und Astrophysik, Munich
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Abstract

Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 1 , 26 March 1970 , pp. 219 - 240
Copyright
© 1970 Cambridge University Press

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References

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