Volume 7, Number 1, Spring 1999
AXISYMMETRIC PARTICLEBEARING
GRAVITY FLOWS ON SLOPING BOTTOMS
T.B. MOODIE AND J.P. PASCAL
Abstract. In this article we present theoretical models
together with modelbased numerical simulations and analytical
work for radially spreading, polydispersed, particlebearing
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
twolayer shallowwater 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 polydispersed
sediment. In contrast to the plane flow case, we find that
for axisymmetric flows an internal bore forms in the single
layer shallowwater 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 finergrained sediment will generate a thinner deposit than
will a flow transporting a suspension of larger particles.
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