AXISYMMETRICAL PARTICLE-DRIVEN GRAVITY CURRENTS

Axisymmetric gravity currents that result when a dense suspension inru des under a lighter ambient fluid are studied theoretically and experi mentally. The dynamics of and deposition from currents flowing over a rigid horizontal surface are determined for the release of either a fi xed volume or a constant flux of a suspension. The dynamics of the cur rent are assumed to be dominated by inertial and buoyancy forces, whil e viscous forces are assumed to be negligible. The fluid motion is mod elled by the single-layer axisymmetric shallow-water equations, which neglect the effects of the overlying fluid. An advective transport equ ation models the distribution of particles in the current, and this di stribution determines the local buoyancy force in the shallow-water eq uations. 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 sublaye r 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 bot h constant-volume and constant-flux, particle-drived gravity currents develop an internal bore which separates a supercritical particle-free region upstream from a subcritical, particle-rich region downstream n ear the head of the current. For the fixed-volume release, an earlier bore is also predicted to occur very shortly after the initial collaps e of the current. This bore transports suspended particles away from t he origin, which results in a maximum in the predicted deposition away from the centre. To test the model several laboratory experiments wer e performed to determine both the radius of an axisymmetric particle-d riven gravity current as a function of time and its deposition pattern for a variety of initial particle concentrations, particle sizes, vol umes and flow rates. For the release of a fixed volume and of a consta nt flux of suspension, the comparisons between the experimental result s and the theroetical predictions are faily good. However, for the cur rent of fixed volume, we did not observe the bore predicted to occur s hortly after the collapse of the current or the resulting maximum in d eposition downstream of the origin. This is unlike the previous study of Bonnecaze et al. (1993) on two-dimensional currents, in which a str ong bore was observed during the slumping phase. The radial extent R o f the deposit from a fixed-volume current is accurately predicted by t he model, and for currents whose particles settle sufficiently slowly, we fine that R= 1.9(g'V-0(3)/v(s)(2))(1/8), where V is the volume of the current, v(s) is the settling velocity of a particle in the suspen sion and g'(0) is the initial reduced gravity of the suspension.