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Volume 7,     Number 1,     Spring 1999

 

AXISYMMETRIC PARTICLE-BEARING
GRAVITY FLOWS ON SLOPING BOTTOMS
T.B. MOODIE AND J.P. PASCAL

Abstract. In this article we present theoretical models together with model-based numerical simulations and analytical work for radially spreading, poly-dispersed, particle-bearing gravity currents moving down inclined surfaces while depositing sediment. With a view to modelling certain naturally occurring events in which the suspended particles have terminal settling velocities which are much less than the fluid velocity and are transported and deposited downslope by means of dilute subsurface currents, we develop our models in the appropriate parametric regime. We find that, in this regime of dilute suspensions, the models consist of either one- or two-layer shallow-water theory depending upon whether or not we wish to include the inertial effects of the upper layer. In either case we find that there is insignificant momentum transfer between fluid and particles so that the particles move essentially with the fluid.
We employ these models to examine various aspects of axisymmetric gravity currents produced when a fixed volume suspension in contact with an end wall of a reservoir is suddenly released and flows downslope depositing poly-dispersed sediment. In contrast to the plane flow case, we find that for axisymmetric flows an internal bore forms in the single layer shallow-water model where backflow in the upper layer is neglected. This new theoretical result appears to be in accord with various experimental observations involving the radial flow of shallow bottom currents. An analysis of shock initiation times was carried out using the arguments of weakly nonlinear geometrical optics. The results of this calculation were compared to numerical solutions of the Cauchy problem and found to be in agreement. We also found that, for a given mass of sediment in the initial suspension, a flow transporting a finer-grained sediment will generate a thinner deposit than will a flow transporting a suspension of larger particles.

 

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