Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T11:49:58.363Z Has data issue: false hasContentIssue false
  • English
  • Français

Source–sink flows in a rotating annulus: a combined laboratory and numerical study

Published online by Cambridge University Press:  29 March 2006

D. A. Bennetts  and
W. D. N. Jackson
D. A. Bennetts
Affiliation:
Meteorological Office, Bracknell, Berkshire, England
W. D. N. Jackson
Affiliation:
Meteorological Office, Bracknell, Berkshire, England
Get access Rights & Permissions [Opens in a new window]

Abstract

A general characteristic of rapidly rotating fluids is that accurate experimental measurements can only be made of the main (azimuthal) flow. The secondary flow is then usually deduced from theory, although this is often incomplete in the boundary regions where the secondary flow is of most interest.

In this paper we consider the case of source-sink flow between the porous walls of a rapidly rotating annular container and numerically integrate the full equations of motion in order to determine the complete structure of the secondary flow. The results are compared with the (approximate) analytic studies of Hide (1968) and Bennetts & Hocking (1973) to show the differences between the two approaches.

A defect of many previous numerical papers has been the inability to check the solution in the nonlinear case. To overcome this, new experimental measurements of the azimuthal velocity profile for a Rossby number of 0·238 have been obtained and these are compared with the numerical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 4 , 11 December 1974 , pp. 689 - 705
Copyright
© 1974 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

Barcilon, V. 1970 Phys. Fluids, 13, 537–544.
Bennetts, D. A. & Hocking, L. M. 1973 Proc. Roy. Soc A 333, 469–489.
Dunst, M. 1972 J. Fluid Mech. 55, 301–310.
Durst, F., Melling, A. & Whitelaw, J. H. 1972 J. Fluid Mech. 56, 143–160.
Greenspan, H. P. & Weinbaum, S. 1965 J. Math. & Phys. 44, 66–85.
Hamel, R. 1916 Jber. dtsch. MatVer. 25, 34–47.
Hide, R. 1968 J. Fluid Mech. 32, 737–764.
Lilly, D. K. 1964 J. Atmos. Sci. 21, 83–98.
Pearson, C. E. 1965 J. Fluid Mech. 21, 611–622.
Phillips, N. A. 1959 In The Atmosphere and the Sea in Motion. (ed. B. Bolin), pp. 501–504. Oxford University Press.
Richardson, L. F. 1922 In Weather Prediction by Numerical Process, p. 236. Cambridge University Press.
Stewartson, K. 1957 J. Fluid Mech. 3, 17–26.
Wedemeyer, F. H. 1964 J. Fluid Mech. 20, 383–399.
Williams, G. P. 1967 J. Atmos. Sci. 24, 144–161.