Turbulent fountains in one- and two-layer crossflows

Abstract

The Lagrangian theory developed for fountains in a stationary fluid is extended to predict the path and breadth of a fountain in a one-and two-layer fluid with a moderate crossflow. The predictions compare well with the results of laboratory experiments of fountains in a one-layer fluid. The empirical spreading parameter determined from the one-layer experiments is used in the theory for fountains in a twolayer crossflow. Though qualitatively correct, the theory underpredicts the height and radius of the fountains. Similar to the behaviour of fountains in two-layer stationary ambients, the fountain in a two-layer crossflow is observed to exhibit three regimes of flow: it may penetrate the interface, eventually returning to the level of the source where it spreads as a propagating gravity current; upon descent, it may be trapped at the interface where it spreads as a propagating intrusion; it may do both, partially descending to the source and partially being trapped at the interface. These regimes are classified theoretically and empirically. The theoretical classification compared the buoyancy excess of the descending flow to the density difference between the two layers. The regimes are also classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid.

Light attenuation experiments on double diffusive plumes and fountains

“…A cubical tank measuring L T = 39.5 cm on each side was filled to a depth H T = 38 cm with either fresh or salt water of density ρ a . This ambient density, measured with the Anton Paar DMA 4500 density meter, ranged in different experiments from ρ a = 0.998 to 1.100 g/cm 3 . Separately, a reservoir was filled with 10 l of fresh or salty water, which ranged between boiling and room temperature.…”

“…In most experiments, the background intensity was approximately uniform having intensities of I 00 = 0.80 ± 0.02 in which 1 was white and 0 black. The attenuation parameter γ was found using (3) in which I s was the intensity of light passing through the plume immediately above the source where d = 0.4 cm and C s ≡ c 0 = 1. Typical values were found to range between γ 1.0 and 2.0 cm −1 .…”

“…As a test of the efficacy of the axisymmetric inversion method, we examined the structure of a forced buoyant plume of fresh water into a uniform but salty ambient of relative density − ρ 0 = ρ a − ρ 00 = 0.0985 g/cm 3 . Both the plume and ambient had the same temperature.…”

“…Figure 9 shows the results of using the light attenuation and probe measurements to determine the density of the fountain experiment shown in Figure 5. The experimental parameters were Q 0 = 1.28 cm 3 /s (hence, w 0 = 10.3 cm/s), S 0 = 4.5 ppt, and T 0 − T a = 12 • C. Hence, the relative densities due separately to salinity and temperature were ρ S0 = 0.0033 g/cm 3 and ρ T0 = −0.0025 g/cm 3 , respectively. The combined relative density at the source, ρ 0 = ρ S0 + ρ T0 = 0.0008 g/cm 3 , was used to compute the corresponding momentum and buoyancy fluxes, M 0 = 13.2 cm 4 /s 2 and F 0 = 1.02 cm 4 /s 3 , respectively.…”

“…The process of understanding the complex problem of sour gas dispersion from flares has inspired several fundamental experimental-theoretical investigations including the study of fountains incident upon a model atmospheric inversion 2 and their evolution in a cross-flow. 3 Here, we take the ambient to be uniform and stationary in order to focus upon the competing effects of positive buoyancy due to heat and negative buoyancy due to the large molecular mass of H 2 S relative to air.…”