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Steady flow in rapidly rotating variable-area rectangular ducts. Part 3. Inertial perturbations for small divergences

Published online by Cambridge University Press:  19 April 2006

J. S. Walker  and
A. M. El-Consul
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois, Urbana
A. M. El-Consul
Affiliation:
Department of Mathematics, University of Al-Fateh, Tripoli, Libya
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Abstract

This paper is part of a series treating the flow in a variable-area, rectangular duct which is rotating about an axis that is perpendicular to the duct's centre-line and parallel to one pair of walls (sides). The speed of rotation is assumed to be sufficiently large that viscous effects are confined to boundary layers and free shear layers and that inertial effects are much smaller than viscous effects everywhere. Earlier papers present inertialess solutions for a prototype with parallel sides everywhere, parallel top and bottom upstream of a cross-section, and straight, symmetrically diverging top and bottom downstream of the same cross-section. The present paper presents inertial perturbations to the inertialess solutions for the prototype when the slope of the diverging top and bottom is small. This paper begins to bridge the gap between papers treating inertialess flows in ducts with arbitrary geometries and papers treating flows with significant inertial effects in ducts with restricted geometries.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 3 , 15 April 1980 , pp. 417 - 434
Copyright
© 1980 Cambridge University Press

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References

Boyer, D. L. 1971 Rotating flow over a step. J. Fluid Mech. 50, 675–687.Google Scholar
Calderon, A. 1976 Steady flow in rapidly rotating rectangular ducts with small divergences. Ph.D. thesis, University of Illinois at Urbana-Champaign.
Calderon, A. & Walker, J. S. 1977 Steady flow in rapidly rotating variable-area rectangular ducts. Part 2. Small divergences. J. Fluid Mech. 81, 353–368.Google Scholar
El-consul, A. M. 1978 Inertial perturbations to inertialess magnetohydrodynamic and rotating flows. Ph.D. thesis, University of Illinois at Urbana-Champaign.
Foster, M. R. 1975 Rotating flow past an elliptic-cylindrical bump of large aspect ratio. Z. angew. Math. Phys. 26, 789–806.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Howard, L. N. 1969 Rotating Flow. Lectures at the Royal Institute of Technology, Stockholm.
Hseuh, Y. & Legeckis, R. 1973 Western intensification in a rotating water tunnel. Geophys. Fluid Dyn. 5, 333–358.Google Scholar
Huppert, H. E. & Stern, M. E. 1974 The effect of side walls on homogeneous rotating flow over two-dimensional obstacles. J. Fluid Mech. 62, 417–436.Google Scholar
Jacobs, S. J. 1964 The Taylor column problem. J. Fluid Mech. 20, 581–591.Google Scholar
Roberts, P. H. 1967 An Introduction to Magnetohydrodynamics. Elsevier.
Vaziri, A. & Boyer, D. L. 1971 Rotating flow over shallow topographies. J. Fluid Mech. 50, 79–95.Google Scholar
Walker, J. S. 1975 Steady flow in rapidly rotating variable-area rectangular ducts. J. Fluid Mech. 69, 209–227.Google Scholar