×

zbMATH — the first resource for mathematics

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.

MSC:
76V05 Reaction effects in flows
76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.