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Axisymmetric withdrawal and inflow in a density-stratified container. (English) Zbl 0585.76171
Summary: 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 \(S=(Q^ 2N/v^ 3)^{1/15}\) 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.

76V05 Reaction effects in flows
76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics
Full Text: DOI
[1] Sharp, J. Hydraul. Div. ASCE 95 pp 811– (1969)
[2] DOI: 10.1017/S0022112074001595 · Zbl 0287.76069 · doi:10.1017/S0022112074001595
[3] Gariel, Houille Blance 4 pp 56– (1949)
[4] Fasham, Oceanogr. Mar. Biol. Ann. Rev. 16 pp 43– (1978)
[5] Didden, J. Fluid Mech. 121 pp 27– (1982)
[6] Craya, Houille Blanche 4 pp 44– (1949) · doi:10.1051/lhb/1949017
[7] DOI: 10.1017/S0022112076002267 · Zbl 0358.76075 · doi:10.1017/S0022112076002267
[8] DOI: 10.1016/0004-6981(79)90078-7 · doi:10.1016/0004-6981(79)90078-7
[9] Blake, J. Volcanol. Geotherm. Res. none pp none– (1985)
[10] DOI: 10.1017/S0022112074001133 · doi:10.1017/S0022112074001133
[11] DOI: 10.1017/S002211206600082X · doi:10.1017/S002211206600082X
[12] Jirka, J. Hydraul. Res. 17 pp 53– (1979)
[13] Ivey, J. Hydraul. Div. ASCE 104 pp 1225– (1978)
[14] DOI: 10.1017/S0022112076002577 · Zbl 0344.76062 · doi:10.1017/S0022112076002577
[15] Huppert, J. Fluid Mech. 121 pp 43– (1982)
[16] Zatsepin, Izv. Atmos. Oceanic Phys. 18 pp 77– (1982)
[17] Spigel, J. Hydraul. Res. 22 pp 35– (1984)
[18] Sharp, J. Hydraul. Div. ASCE 95 pp 1771– (1969)
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