ALBERT

Description: Axisymmetric gravity currents that result when a dense suspension intrudes under a lighter ambient fluid are studied theoretically and experimentally. The dynamics of and deposition from currents flowing over a rigid horizontal surface are determined for the release of either a fixed volume or a constant flux of a suspension. The dynamics of the current are assumed to be dominated by inertial and buoyancy forces, while viscous forces are assumed to be negligible. The fluid motion is modelled by the single-layer axisymmetric shallow-water equations, which neglect the effects of the overlying fluid. An advective transport equation models the distribution of particles in the current, and this distribution determines the local buoyancy force in the shallow-water equations. The transport equation is derived on the assumption that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through a viscous sublayer at the bottom of the current. No adjustable parameters are needed to specify the theoretical model. The coupled equations of the model are solved numerically, and it is predicted that after an early stage both constant-volume and constant-flux, particle-driven gravity currents develop an internal bore which separates a supercritical particle-free region upstream from a subcritical particle-rich region downstream near the head of the current. For the fixed-volume release, an earlier bore is also predicted to occur very shortly after the initial collapse of the current. This bore transports suspended particles away from the origin, which results in a maximum in the predicted deposition away from the centre.To test the model several laboratory experiments were performed to determine both the radius of an axisymmetric particle-driven gravity current as a function of time and its deposition pattern for a variety of initial particle concentrations, particle sizes, volumes and flow rates. For the release of a fixed volume and of a constant flux of suspension, the comparisons between the experimental results and the theoretical predictions are fairly good. However, for the current of fixed volume, we did not observe the bore predicted to occur shortly after the collapse of the current or the resulting maximum in deposition downstream of the origin. This is unlike the previous study of Bonnecaze et al. (1993) on two-dimensional currents, in which a strong bore was observed during the slumping phase. The radial extent R of the deposit from a fixed-volume current is accurately predicted by the model, and for currents whose particles settle sufficiently slowly, we find that R = 1.9(g′0V3 / v2s)1/8, where V is the volume of the current, vs is the settling velocity of a particle in the suspension and g’0 is the initial reduced gravity of the suspension.

Description: The motion of instantaneous and maintained releases of buoyant fluid through shallow permeable layers of large horizontal extent is described by a nonlinear advection-diffusion equation. This equation admits similarity solutions which describe the release of one fluid into a horizontal porous layer initially saturated with a second immiscible fluid of different density. Asymptotically, a finite volume of fluid spreads as t1/3. On an inclined surface, in a layer of uniform permeability, a finite volume of fluid propagates steadily alongslope under gravity, and spreads diffusively owing to the gravitational acceleration normal to the boundary, as on a horizontal boundary. However, if the permeability varies in this cross-slope direction, then, in the moving frame, the spreading of the current eventually becomes dominated by the variation in speed with depth, and the current length increases as t112. Shocks develop either at the leading or trailing edge of the flows depending upon whether the permeability increases or decreases away from the sloping boundary. Finally we consider the transient and steady exchange of fluids of different densities between reservoirs connected by a shallow long porous channel. Similarity solutions in a steadily migrating frame describe the initial stages of the exchange process. In the final steady state, there is a continuum of possible solutions, which may include flow in either one or both layers of fluid. The maximal exchange flow between the reservoirs involves motion in one layer only. We confirm some of our analysis with analogue laboratory experiments using a Hele-Shaw cell. © 1995, Cambridge University Press. All rights reserved.

Description: Axisymmetric gravity currents in a system rotating around a vertical axis, that result when 3 dense fluid intrudes horizontally under a less dense ambient fluid, are studied. Situations for which the density difference between the fluid is due either to compositional differences or to suspended particulate matter are considered. The fluid motion is described theoretically by the inviscid shallow-water equations. A 'diffusion' equation for the volume fraction in the suspension is derived for the particle-driven case, and two different models for this purpose are presented. We focus attention on situations in which the apparent importance of the Coriolis terms relative to the inertial terms, represented by the parameter script c sign (the inverse of a Rossby number), is not large. Numerical and asymptotic solutions of the governing equations clarify the essential features of the flow field and particle distribution, and point out the striking differences from the non-rotating case (Bonnecaze, Huppert & Lister 1995). It is shown that the Coriolis effects eventually become dominant; even for small script c sign, Coriolis effects are negligible only during an initial period of about one tenth of a revolution. Thereafter the interface of the current acquires a shape which has a downward decreasing profile at the nose and its velocity of propagation begins to decrease to zero more rapidly than in the non-rotating situation. This relates the currents investigated here to the previously studied quasi-steady oceanographic structures called rings, eddies, vortices or lenses, and may throw additional light on the dynamics of their formation. The theoretical results were tested by some preliminary experiments performed in a rotating cylinder of diameter 90 cm filled with a layer of water of depth 10 cm in which a cylinder of heavier saline fluid of diameter 9.4 cm was released.

Description: The propagation at high Reynolds number of a heavy, two-dimensional gravity current of given initial volume at the base of a uniform flow is considered. An experimental setup is described for which a known volume of fluid is rapidly introduced halfway down a 9m channel in which there is a uniform flow of water. The density excess of the released fluid is produced by either dissolving salt or suspending particles in water. The upstream and downstream propagation of the current was measured for different initial salt concentrations, particle sizes and concentrations. A simple box model for the motion of and deposit from the gravity current is constructed. The analytical results obtained compare well with our numerical solutions of one-layer and two-layer models incorporating the appropriate shallow-water equations. Both sets of results are in very good agreement with the experimental data.

Description: Many flows, including those containing suspended particles, are kept turbulent by the action of the bottom stress, and this turbulence is also responsible for maintaining sedimenting particles in suspension and in some cases entraining more particles from the bed. A convenient one-dimensional analogue of these processes is provided by laboratory experiments conducted in a mixing box, where a characterizable turbulence is generated by the vertical oscillation of a horizontal grid. In the present paper we report the results of a series of experiments with a grid located close to the bottom boundary to simulate the action of stresses acting at a rough boundary, and compare the results with those obtained using the more extensively studied geometry in which a similar grid is located in the interior of a stirred fluid layer. Experiments have been conducted both with dense, particle-free fluid layers and with layers containing sufficiently high concentrations of dense particles to have a significant effect on the bulk density. In the fluid case, the interface at the top of the stirred dense layer continues to rise as lighter fluid is entrained across the interface. Sediment layers are distinctly different, because the particles responsible for the density difference between the layers can fall out of the suspension as it changes in thickness. The work done in keeping particles in suspension and the effect of this on the turbulence above the grid must be taken into account. The mechanism of resuspension of particles depends on the level of turbulence near the bottom boundary, below the grid. As the stirring rate, and thus the intensity of turbulence, are increased three possible equilibrium states can be attained sequentially: the particles eventually all precipitate; or some particles precipitate while the remainder are held indefinitely in suspension; or all the particles are suspended. In the last two cases a stable, self-limited suspension layer is produced, separated from the overlying fluid by a sharp density interface at a fixed height. Theoretical arguments are presented which provide a satisfactory scaling of the experimental data. These are compared with previous theories and numerical experiments aimed at modelling both the one-dimensional problem and the corresponding processes in turbulent gravity currents. Comparisons are also made with sediment-laden channel flows and convecting layers containing sedimenting particles. Similar results will hold for light, positively buoyant particles or non-coalescing bubbles. © 1995, Cambridge University Press. All rights reserved.

Description: We analyse the complete solidification from a side boundary of a finite volume of a binary alloy. Particular emphasis is placed upon the compositional stratification produced in the solid, the structure of which is determined by the competition between the rates of solidification and of laminar box filling by the fractionated fluid released at the solid/liquid interface. It is demonstrated by scaling arguments that numerical calculations performed at relatively low values of the Rayleigh and Lewis numbers may be used to describe equally well laboratory experiments previously performed at moderate Rayleigh and Lewis numbers and the high-Rayleigh-number, high-Lewis-number convective regime expected during the solidification of a large magmatic body, provided that the balance between solidification and laminar box filling is maintained. This balance can be represented by a single dimensionless group of parameters. The boundary-layer analysis is extended to fluids whose viscosity is strongly dependent upon temperature and composition, and an effective viscosity is derived which may be used to describe both the magnitude and pattern of compositional stratification in the solid. © 1995, Cambridge University Press. All rights reserved.