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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
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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

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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.