Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T02:35:54.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydraulic control by a wide weir in a rotating fluid

Published online by Cambridge University Press:  29 March 2006

E. Sambuco  and
J. A. Whitehead
E. Sambuco
Affiliation:
Department of Meteorology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Present address: Hydronautics, Incorporated, Laurel, Maryland 20810.
J. A. Whitehead
Affiliation:
Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
Get access Rights & Permissions [Opens in a new window]

Abstract

Flow control by a wide, deep weir in a rotating fluid is investigated theoretically and experimentally. A strong (vertical) vorticity constraint due to frame rotation is combined with conservation of the Bernoulli function along streamlines and a standard hydraulic control assumption to show that the volume flux over the barrier is \[ Q = g^{-1}\left[\frac{2}{3}g(H - b_0)-\frac{1}{3}f^2l^2 \right]^{\frac{3}{2}}, \] where H is the depth of the fluid column upstream, bo is the crest height, f is the Coriolis parameter, and l is a length-scale measure of the breadth of the weir. The component of the velocity parallel to the weir crest is computed from conservation of potential vorticity to be v = −fl; perpendicular to the crest, we recover the standard hydraulic relation u = (gh0)½.

Experimental investigations of upstream height and streamline deflexion as functions of rotation are described. It is found that agreement with theory is good up to a certain rate of rotation, above which the finite width of the experimental weir becomes important.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 3 , 10 February 1976 , pp. 521 - 528
Copyright
© 1976 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

Charney, J. G. 1955 Proc. Nat. Acad. Sci. 41, 731–810.
Houghton, D. D. & Kasahara, A. 1968 Comm. Pure Appl. Math. 21, 1–810.
Long, R. R. 1954 Tellus 6, 98–810.
Stern, M. 1975 Ocean Circulation Physics. Academic.
Whitehead, J. A., Leetmaa, A. & Knox, R. A. 1974 Geophys. Fluid Dyn. 6, 101–810.