Gravity currents

Benjamin TB (1968) Gravity currents and related phenomena. J. Fluid Mechanics 31(2) 209-248 Butterworth D (1975) A comparison of some void-fraction relationships for co-current gas-liquid flow. Int J Multiphase Flow 1 845-850... 

Bercovici D, Lin J (1996) A gravity current model of cooling mantle plume heads with temperature dependent buoyancy and viscosity. J Geophys Res 101 3291-3309 Blundy J, Wood B (1994) Prediction of crystal-melt partition coefficients from elastic moduh. Nature 372 452-454... 

McCarthy, K.L. and Seymour, J.D. 1994. Gravity current analysis of the Bostwick consistometer for power law foods. J. Texture Stud. 25 207-220. 

Rehm, R.G., McGrattan, K.B., Baum, H.R., and Cassel, K.W. Transport by gravity currents in building fires. In Fire Safety Science—Proceedings of the Fifth International Symposium. Boston, MA International Association for Fire Safety Science, 1997, pp. 391 —402. 

Huppert, H. 1982. The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. Joumcd of Fluid Mechanics, 121, 43-58. 

The static stability of the air stream usually changes as it moves into and out of the urban area, typically becoming less and more stable, respectively. However it should not be assumed that the boundary layer profiles over the urban area and downwind are identical to the equilibrium states found in neutral, stable and unstable boundary layers over flat terrain. In fact as the flow adjusts characteristic distortions of the air flow profiles occur on these scales, such as blocked flow, unsteady slope flows, gravity currents and boundary layer jets especially near hills, coasts and urban/rural boundaries. These distorted profiles (which are ignored in most mesoscale atmospheric models) significantly affect dispersion (e.g. Hogstrom and Smedman, [274] Owinoh et al., [477]). 

With Fr 1 globally, the flow in the Wind Tunnel model study divided into two distinct flow regimes. Above the canopy the flow remained fully turbulent but stably stratified with a gradient Richardson number Ri 0.1. Within the canopy, the flow was laminar with Ri 10 and flowed downhill as gravity currents on both the windward... 

Figure 2-8. A sketch of the profiles of constant hydrostatic pressure near the nose of a gravity current. Because of the horizontal gradients of hydrostatic pressure within the nose region, it will propagate to the right, displacing the exterior fluid as it goes.

Problem 6-1. Gravity-Driven Flow of a Thin Film. Consider the gravity-driven flow of a thin layer of Newtonian fluid (a so-called gravity current) on an inclined plane of angle 0 to the horizontal. 

As a model for this transport process, consider the axisymmetric spreading of a fluid of density p + Ap in a porous media containing a fluid of density/ ). Assume the fluid spreads out over an impermeable bottom and that the volume of the dense fluid or gravity current is given by Qta, where t is time. The viscosity of the gravity current is p. and the permeability of the porous medium is k. Also, neglect the effects of capillary forces and assume the flow is dominated by a balance between buoyancy and viscous forces. This balance of forces in a porous medium is described by Darcy s equations, which are given by... 

Determine the pressure field within the gravity current. Use Darcy s law to find the radial velocity as a function of the height of the gravity current, h(r,t). 

Another method that has received attention is injecting a dense C02-seawater mixture at a depth of 500-1000 m, forming a sinking bottom gravity current. C02-enriched seawater is less than 1% heavier than seawater, but this is sufficient to promote a sinking density current, especially if the current were formed along a submarine canyon. However, the environmental impacts would be greater with this option due to the concentrated nature of the plume, and its contact with the seafloor. 

G—Gibbs free energy g—acceleration due to gravity /—current Ii—limiting current Ip—peak current... 

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