Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T21:14:52.618Z Has data issue: false hasContentIssue false
  • English
  • Français

The hydraulics of rotating-channel flow

Published online by Cambridge University Press:  11 April 2006

A. E. Gill
A. E. Gill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Flow of a homogeneous inviscid fluid down a rotating channel of slowly varying crosssection is considered, with particular reference to conditions under which the flow is ‘hydraulically controlled’. This problem is a member of a general class of problems of which gas flow through a nozzle and flow over a broad-crested weir are examples (Binnie 1949). A general discussion of such problems gives the means for determining the position of the control section (which is generally flow dependent) and shows that at this position there always exist long-wave disturbances with zero phase speed (i.e. disturbances are always ‘critical’ at the control section). The general theory is applied to the rotating-channel problem for the case of uniform potential vorticity. For this problem, three parameters are needed to specify the upstream flow, and the control theory gives a relationship between these parameters which depends on the geometry of the channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 4 , 23 May 1977 , pp. 641 - 671
Copyright
© 1977 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

Binnie, A. M. 1949 Proc. Roy. Soc. A 197, 545.
Gill, A. E. 1976 J. Fluid Mech. 77, 603.
Gill, A. E. & Clarke, A. J. 1974 Deep-Sea Res. 21, 325.
Hugoniot, P. H. 1886 C. R. Acad. Sci., Paris 103, 1178.
Long, R. R. 1972 Ann. Rev. Fluid Mech. 4, 69.
Reynolds, O. 1886 Phil. Mag. (5) 21, 185.
Sambuco, E. & Whitehead, J. A. 1976 J. Fluid Mech. 73, 521.
Smith, P. C. 1975 Deep-Sea Res. 22, 853.
Stalcup, M. C., Metcalf, W. G. & Johnson, R. G. 1975 J. Mar. Res. Suppl. 33, 15.
Stern, M. E. 1974 Geophys. Fluid Dyn. 6, 127.
Stern, M. E. 1976 Ocean Circulation Physics. Academic Press.
Whitehead, J. A., Leetmaa, A. & Knox, R. A. 1974 Geophys. Fluid Dyn. 6, 101.