Surface Expression of a Wall Fountain: Application to Subglacial Discharge Plumes

We use laboratory experiments and theoretical modeling to investigate the surface expression of a subglacial discharge plume, as occurs at many fjords around Greenland. The experiments consider a fountain that is released vertically into a homogeneous fluid, adjacent either to a vertical or a sloping wall, that then spreads horizontally at the free surface before sinking back to the bottom. We present a model that separates the fountain into two separate regions: a vertical fountain and a horizontal, negatively buoyant jet. The model is compared to laboratory experiments that are conducted over a range of volume fluxes, density differences, and ambient fluid depths. It is shown that the nondimensionalized length, width, and aspect ratio of the surface expression are dependent on the Froude number, calculated at the start of the negatively buoyant jet. The model is applied to observations of the surface expression from a Greenland subglacial discharge plume. In the case where the discharge plume reaches the surface with negative buoyancy the model can be used to estimate the discharge properties at the base of the glacier.

Particle fountains in a confined environment

We present new experiments and theoretical models of the motion of relatively dense particles carried upwards by a liquid jet into a laterally confined space filled with the same liquid. The incoming jet is negatively buoyant and rises to a finite height, at which the dense mixture of liquid and particles, diluted by the entrainment of ambient liquid, falls back to the floor. The mixture further dilutes during the collapse and then spreads out across the floor and supplies an up-flow outside the fountain equal to the source volume flux plus the total entrained volume flux. The fate of the particles depends on the particle fall speed, $u_{fall}$ , compared to (i) the characteristic fountain velocity in the fountain core, $u_{F}$ , (ii) the maximum upward velocity in the ambient fluid outside the fountain, $u_{u}(0)$ , which occurs at the base of the fountain, and (iii) the upward velocity in the ambient fluid above the top of the fountain associated with the original volume flux in the liquid jet, $u_{BG}$ . From this comparison we identify four regimes. (I) If $u_{fall}>u_{F}$ , then the particles separate from the fountain and settle on the floor. (II) If $u_{F}>u_{fall}>u_{u}(0)$ , the particles are carried to the top of the fountain but then settle as the collapsing flow around the fountain spreads out across the floor; we do not observe particle suspension in the background flow. (III) For $u_{u}(0)>u_{fall}>u_{BG}$ we observe a particle-laden layer outside the fountain which extends from the floor of the tank to a point below the top of the fountain. The density of this lower particle-laden layer equals the density of the collapsing fountain fluid as it passes downwards through this interface. The collapsing fluid then spreads out horizontally through the depth of this particle-laden layer, instead of continuing downwards around the rising fountain. In the lower layer, the negatively buoyant source fluid in fact rises as a negatively buoyant jet, but this transitions into a fountain above the upper interface of the particle-laden layer. The presence of the particles in the lower layer reduces the density difference between fountain and environment, leading to an increase in the fountain height. (IV) If $u_{fall}<u_{BG}$ then an ascending front of particles rises above the fountain and eventually fills the entire tank up to the level where fluid is removed from the tank. We compare the results of a series of new laboratory experiments with simple theoretical investigations for each case, and discuss the relevance of our results.

An Investigation on the Effects of Different Stratifications on Negatively Buoyant Jets

Negatively buoyant jets develop when fluids are released upwards into a lighter fluid or, vice versa, downwards into a heavier fluid. There are many engineering applications, such as the discharge, via submerged outfalls, of brine from desalination plants into the sea. Some concerns are raised about the potential negative environmental impacts of this discharge. The increase in salinity is the major cause for environmental impact, as it is very harmful to many marine species. The diffusers for brine discharge are typically inclined upwards, to increase the path before the brine reaches the sea bottom, as it tends to fall downwards driven by negative buoyancy. The negatively buoyant jet that develops conserves axisymmetry only when released vertically, so that it is not possible to use the well-known equations for axisymmetric jets. The main target of this paper is to investigate on a laboratory model the effects of different stratifications on the features of negatively buoyant jets. This has been done via a LIF (Light Induced Fluorescence) technique, testing various release angles on the horizontal and densimetric Froude numbers. Except for the initial stage, a different widening rate for the upper boundary and the lower boundary has been highlighted.

Forced turbulent fountain flow behaviour

Numerical simulations of turbulent fountain flow are used to investigate the important energy and mass transfer mechanisms present in the forced fountain flow regime, which has been reported to exist at Froude numbers (Fr) greater than 3. The flow is equivalent to a negatively buoyant jet with three flow streams, the inner upflow (IF), the outer downflow (OF) and the surrounding ambient fluid (AF). Simulation results are presented forFr= 4 and 7 at Reynolds numberRe= 3350. The mean fountain penetration height scales with the previously reported relationZm/R0= 2.46Fr, whereR0is the source radius, but the assumptions behind analytical derivations of the relation are not supported by the present results. The results suggest that the OF may be relatively well described by the dynamics of a pure line plume surrounding the IF but with higher entrainment owing to the unsteady pulsing behaviour of the flow entering the OF from the IF. The length scale for a pure plume appears to apply atFr= 7 in the OF and a degree of self-similarity exists. Comparisons with previous results suggest the IF is not fully developed atFr= 7 and entrainment into the IF from the OF may not occur untilFr> 15.

Simulation of temperature influence on flow pattern and residence time in a detention tank

Three-dimensional simulations were used to model how a temperature difference between the incoming water and tank water influences the flow pattern and residence time in a detention tank. Buoyant, neutrally buoyant and negatively buoyant incoming jets were simulated. The simulations were compared with measurements for neutrally buoyant jets in a large-scale model of a detention tank (13 × 9×1 m). The results show that a negatively buoyant jet gives slightly less effective volume, defined as the time when 50% of added tracer has passed the outlet divided by the nominal residence time, than a neutrally buoyant jet. The flow pattern for a negatively buoyant jet at low densimetric Froude numbers consists of a current that travels along the bottom towards the outlet and a counter current at the surface towards the inlet, while the neutrally buoyant jet excites a surface jet with two large eddies on each side of the jet. This implies that the short-circuiting will decrease when a negatively buoyant jet at low densimetric Froude number occurs in the tank. The difference between the flow pattern excited by a buoyant jet and a neutrally buoyant jet is small.