Armi, L.; Farmer, D. M. Maximal two-layer exchange through a contraction with barotropic net flow. (English) Zbl 0587.76168 J. Fluid Mech. 164, 27-51 (1986). The gravitational exchange of two fluids with different densities between reservoirs connected by a channel of constant depth and slowly varying breadth is analysed as a problem of internal hydraulics. It is shown that maximal two-way exchange with a net barotropic flow requires the presence of two controls, one at the narrowest section and a second or ’virtual’ control lying to one side of the narrowest section. The two controls are connected by a subcritical region, but are separated from subcritical conditions in the reservoirs by supercritical flow and stationary internal bores. Solutions are found for maximal exchange without a net barotropic component, in which case the problem is similar to that first examined by H. Stommel and H. G. Farmer [J. Mar. Res. 12, 13- 20 (1953)]. The Stommel & Farmer analysis is shown to be a rather special limiting example of submaximal exchange, not generally applicable to natural flows. The addition of a net barotropic flow yields a range of different flow types, including maximal exchange, one-layer baroclinic flow, one-layer barotropic flow, submaximal flow governed by a reservoir condition and two-layer unidirectional flow. The maximal-exchange solution is integrated for periodic barotropic flow. Cited in 3 ReviewsCited in 24 Documents MSC: 76T99 Multiphase and multicomponent flows 76M99 Basic methods in fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:gravitational exchange of two fluids; reservoirs connected by a channel; problem of internal hydraulics; maximal two-way exchange; net barotropic flow; subcritical region; subcritical conditions; supercritical flow; stationary internal bores; submaximal exchange; one-layer baroclinic flow; one-layer barotropic flow; submaximal flow; reservoir condition; two-layer unidirectional flow; maximal-exchange solution; periodic barotropic flow PDFBibTeX XMLCite \textit{L. Armi} and \textit{D. M. Farmer}, J. Fluid Mech. 164, 27--51 (1986; Zbl 0587.76168) Full Text: DOI References: [1] DOI: 10.1017/S0022112068000133 · Zbl 0169.28503 · doi:10.1017/S0022112068000133 [2] Assaf, Deep-Sea Res. 21 pp 947– (1974) [3] Armi, Oceanologica Acta 8 pp 37– (1985) [5] DOI: 10.1017/S0022112070001544 · doi:10.1017/S0022112070001544 [6] Stommel, J. Mar. Res. 12 pp 13– (1953) [7] Stommel, J. Mar. Res. 11 pp 205– (1952) [8] Long, J. Met. 13 pp 70– (1956) · doi:10.1175/1520-0469(1956)013<0070:LWIATF>2.0.CO;2 [10] Murray, J. Mar. Res. 42 pp 265– (1984) [11] Bryden, Oceanologica Acta 7 pp 289– (1984) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.