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Axisymmetric withdrawal and inflow in a density-stratified container

Published online by Cambridge University Press:  21 April 2006

G. N. Ivey  and
S. Blake
G. N. Ivey
Affiliation:
Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra, A.C.T. 2601
S. Blake
Affiliation:
Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra, A.C.T. 2601
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Abstract

The axisymmetric withdrawal of fluid from a linearly stratified container is studied over the full parameter range. When only buoyancy and inertia are important the flow in the withdrawal layer is influenced by a virtual control point and is not analogous to that observed in the two-dimensional withdrawal problem. Two further flow regimes are shown to exist in which viscous forces are important: one in which convection of species is important, and a second in which diffusion of species is important. Theoretical arguments and laboratory experiments are used to show that $S = (Q^2N/\nu^3)^{\frac{1}{15}}$ is the appropriate flow parameter to differentiate between these possibilities. It is also argued that these results may be generalized to describe the features of several related flows: axisymmetric drawdown (or drawup) in withdrawal from a layered density structure, axisymmetric inflow into a linearly stratified environment and the axisymmetric spreading of density currents.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 161 , December 1985 , pp. 115 - 137
Copyright
© 1985 Cambridge University Press

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References

Blake, S. & Ivey, G. N. 1985 Magma mixing and the dynamics of withdrawal from stratified reservoirs. J. Volcanol. Geotherm. Res. (to be published).Google Scholar
Britter, R. E. 1979 The spread of a negatively buoyant plume in a calm environment. Atmos. Environ. 13, 1241–1247.Google Scholar
Bryant, P. J. & Wood, I. R. 1976 Selective withdrawal from a layered fluid. J. Fluid Mech. 77, 581–591.Google Scholar
Chen, J.-C. 1980 Studies on gravitational spreading currents. Rep. KH-R-40, Calif. Inst. Tech.
Craya, A. 1949 Recherches théoretiques sur l'écoulement de couches superposées de fluides de densités différentes. Houille Blanche 4, 44–55.Google Scholar
Didden, N. & Maxworthy, T. 1982 The viscous spreading of plane and axisymmetric gravity currents. J. Fluid Mech. 121, 27–42.Google Scholar
Fasham, M. J. R. 1978 The statistical and mathematical analysis of plankton patchiness. Oceanogr. Mar. Biol. Ann. Rev. 16, 43–79.Google Scholar
Gariel, P. 1949 Recherches expérimentales sur l'écoulement de couches superposées de fluides de densités différentes. Houille Blance 4, 56–64.Google Scholar
Harleman, D. R. F., Morgan, R. L. & Purple, R. A. 1959 Selective withdrawal from a vertically stratified fluid. In Proc. 8th Congr. IAHR, Montreal, pp. 10-C–1–10-C–16.
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.Google Scholar
Imberger, J. 1980 Selective withdrawal: a review. In Proc. 2nd Intl Symp. on Stratified Flows, Trondheim, pp. 381–400. Tapir.
Imberger, J., Thompson, R. O. R. Y. & Fandry, C. 1976 Selective withdrawal from a finite rectangular tank. J. Fluid Mech. 78, 489–512.Google Scholar
Ivey, G. & Imberger, J. 1978 Field investigation of selective withdrawal. J. Hydraul. Div. ASCE 104, 1225–1237.Google Scholar
Jirka, G. H. & Katalova, D. S. 1979 Supercritical withdrawal from two-layered fluid systems, Part 2. Three-dimensional flow into a round intake. J. Hydraul. Res. 17, 53–62.Google Scholar
Koh, R. C. Y. 1966 Viscous stratified flow towards a sink. J. Fluid Mech. 24, 555–575.Google Scholar
Lawrence, G. A. 1980 Selective withdrawal through a point sink. In Proc. 2nd Intl Symp. on Stratified Flows, Trondheim, pp. 411–425. Tapir.
Lawrence, G. A. & Imberger, J. 1979 Selective withdrawal through a point sink in a continuously stratified fluid with a pycnocline. Rep. ED-79–002, Univ. W. Australia.
McEwan, A. D. & Baines, P. G. 1974 Shear fronts and an experimental stratified shear flow. J. Fluid Mech. 63, 257–272.Google Scholar
Maxworthy, T. 1972 Experimental and theoretical studies of horizontal jets in a stratified fluid. In Proc. Intl Symp. on Stratified Flows, Novosibirsk, pp. 611–618.
Mullin, J. W. 1972 Crystallization. Butterworth.
Pao, H. P. & Kao, T. W. 1974 Dynamics of establishment of selective withdrawal of a stratified fluid from a line sink. Part 1. Theory. J. Fluid Mech. 65, 657–688.Google Scholar
Sharp, J. J. 1969a Spread of buoyant jets at the free surface. J. Hydraul. Div. ASCE 95, 811–825.Google Scholar
Sharp, J. J. 1969b Spread of buoyant jets at the free surface - II. J. Hydraul. Div. ASCE 95, 1771–1773.Google Scholar
Spigel, R. A. & Farrant, B. 1984 Selective withdrawal through a point sink and pynocline formation in a linearly stratified flow. J. Hydraul. Res. 22, 35–51.Google Scholar
Zatsepin, A. G. & Shapiro, G. I. 1982 A study of axisymmetric intrusions into a stratified fluid. Izv. Atmos. Oceanic Phys. 18, 77–80.Google Scholar