Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-20T06:06:43.700Z Has data issue: false hasContentIssue false
  • English
  • Français

Side-wall boundary layers in rotating axial flow

Published online by Cambridge University Press:  29 March 2006

L. G. Redekopp
L. G. Redekopp
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles
Get access Rights & Permissions [Opens in a new window]

Abstract

The boundary layers forming on the walls of an aligned cylinder in a rotating fluid in axial motion are studied theoretically. The analysis shows that the side-wall boundary layer is of the Blasius type when the Rossby number exceeds the inverse square root of the Reynolds number and is transformed to the Stewartson $\frac{1}{3}$-layer when the Rossby number is less than this value. A second thicker boundary layer is superimposed on the $\frac{1}{3}$-layer whenever the difference between the azimuthal velocities of the ambient fluid and the boundary exceeds the axial velocity. Its thickness varies according to the relative magnitudes of these velocities and yields the Stewartson ¼-layer thickness only when the ratio of the azimuthal velocity difference to the axial velocity is of order E⅙, where E is the Ekman number. A uniformly valid solution is obtained for the first case when the boundary layer is of the Blasius type.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 3 , 10 October 1972 , pp. 565 - 576
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, D. J. 1967 Shear layers in a rotating fluid. J. Fluid Mech. 29, 165–176.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Kelly, R. E. & Redekopp, L. G. 1970 The development of horizontal boundary layers in stratified flow. Non-diffusive flow. J. Fluid Mech. 42, 497–512.Google Scholar
Maxworthy, T. 1970 The flow created by a sphere moving along the axis of a rotating slightly viscous fluid. J. Fluid Mech. 42, 497–512.Google Scholar
Miles, J. W. 1972 Axisymmetric rotating flow past a circular disk. J. Fluid Mech. 53, 689–700.Google Scholar
Orloff, K. L. 1971 Experimental investigation of upstream influence in a rotating flow field. Ph.D. thesis, University of California, Santa Barbara.
Rosenhead, L. (ed.) 1963 Laminar Boundary Layers. Oxford University Press.
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17–26.Google Scholar
Van Dyke, M. 1969 Higher-order boundary layer theory. Annual Reviews of Fluid Mechanics, vol. 1 (ed. W. R. Sears), pp. 265–292.