On axisymmetric intrusive gravity currents: The approach to self-similarity solutions of the shallow-water equations in a stratified ambient

2008 ◽  
Vol 237 (14-17) ◽  
pp. 2162-2166
Author(s):  
T. Zemach ◽  
M. Ungarish
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Self Similarity ◽  
Intrusive Gravity Currents

scholarly journals Axisymmetric particle-driven gravity currents

1995 ◽  
Vol 294 ◽  
pp. 93-121 ◽  
Author(s):  
Roger T. Bonnecaze ◽  
Mark A. Hallworth ◽  
Herbert E. Huppert ◽  
John R. Lister
Keyword(s):  
Transport Equation ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Gravity Current ◽  
Gravity Currents ◽  
Mean Flow ◽  
Constant Flux ◽  
Coupled Equations ◽  
Fixed Volume ◽  
Free Region

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.

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