The effect of confining boundaries on viscous gravity currents

2007 ◽  
Vol 577 ◽  
pp. 495-505 ◽  
Author(s):  
DAISUKE TAKAGI ◽  
HERBERT E. HUPPERT
Keyword(s):  
Laboratory Experiments ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Mathematical Equations ◽  
Inclined Channels

Newtonian viscous gravity currents propagating along horizontal and inclined channels with semicircular and V-shaped boundaries are examined. Similarity solutions are obtained from the governing mathematical equations and compared with closely matching data from laboratory experiments in which the propagation of glycerine along different channels was recorded. Geological applications of the results are discussed briefly.

The effects of drag on turbulent gravity currents

2000 ◽  
Vol 416 ◽  
pp. 297-314 ◽  
Author(s):  
LYNNE HATCHER ◽  
ANDREW J. HOGG ◽  
ANDREW W. WOODS
Keyword(s):  
Analytical Solution ◽  
Laboratory Experiments ◽  
Gravity Current ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Flow Speed ◽  
Series Solutions ◽  
Accurate Approximation ◽  
New Class ◽  
Power Series Solutions

We model the propagation of turbulent gravity currents through an array of obstacles which exert a drag force on the flow proportional to the square of the flow speed. A new class of similarity solutions is constructed to describe the flows that develop from a source of strength q0tγ. An analytical solution exists for a finite release, γ = 0, while power series solutions are developed for sources with γ > 0. These are shown to provide an accurate approximation to the numerically calculated similarity solutions. The model is successfully tested against a series of new laboratory experiments which investigate the motion of a turbulent gravity current through a large flume containing an array of obstacles. The model is extended to account for the effects of a sloping boundary. Finally, a series of geophysical and environmental applications of the model are discussed.

scholarly journals Existence and features of similarity solutions for non-Boussinesq gravity currents

2007 ◽  
Vol 226 (1) ◽  
pp. 32-54 ◽  
Author(s):  
C. Ancey ◽  
S. Cochard ◽  
M. Rentschler ◽  
S. Wiederseiner
Keyword(s):  
Gravity Currents ◽  
Similarity Solutions

Laboratory experiments and shallow water simulations of gravity currents moving on flat and up-sloping beds

2014 ◽  
pp. 89-95
Author(s):  
C Adduce ◽  
V Lombardi ◽  
G Sciortino ◽  
M La Rocca ◽  
M Morganti
Keyword(s):  
Shallow Water ◽  
Laboratory Experiments ◽  
Gravity Currents

Propagation of viscous currents on a porous substrate with finite capillary entry pressure

2016 ◽  
Vol 801 ◽  
pp. 65-90 ◽  
Author(s):  
Roiy Sayag ◽  
Jerome A. Neufeld
Keyword(s):  
Laboratory Experiments ◽  
Gravity Current ◽  
Fluid Pressure ◽  
Analytical Techniques ◽  
Gravity Currents ◽  
Porous Substrate ◽  
Entry Pressure ◽  
Self Similar ◽  
Capillary Entry Pressure ◽  
Theoretical Results

We study the propagation of viscous gravity currents over a thin porous substrate with finite capillary entry pressure. Near the origin, where the current is deep, propagation of the current coincides with leakage through the substrate. Near the nose of the current, where the current is thin and the fluid pressure is below the capillary entry pressure, drainage is absent. Consequently the flow can be characterised by the evolution of drainage and fluid fronts. We analyse this flow using numerical and analytical techniques combined with laboratory-scale experiments. At early times, we find that the position of both fronts evolve as $t^{1/2}$, similar to an axisymmetric gravity current on an impermeable substrate. At later times, the growing effect of drainage inhibits spreading, causing the drainage front to logarithmically approach a steady position. In contrast, the asymptotic propagation of the fluid front is quasi-self-similar, having identical structure to the solution of gravity currents on an impermeable substrate, only with slowly varying fluid flux. We benchmark these theoretical results with laboratory experiments that are consistent with our modelling assumption, but that also highlight the detailed dynamics of drainage inhibited by finite capillary pressure.

Entraining gravity currents

2013 ◽  
Vol 731 ◽  
pp. 477-508 ◽  
Author(s):  
Christopher G. Johnson ◽  
Andrew J. Hogg
Keyword(s):  
Richardson Number ◽  
Solution Structure ◽  
Large Scale ◽  
Gravity Current ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Water Model ◽  
Experimental Measurements ◽  
Entrainment Rate ◽  
Long Time

AbstractEntrainment of ambient fluid into a gravity current, while often negligible in laboratory-scale flows, may become increasingly significant in large-scale natural flows. We present a theoretical study of the effect of this entrainment by augmenting a shallow water model for gravity currents under a deep ambient with a simple empirical model for entrainment, based on experimental measurements of the fluid entrainment rate as a function of the bulk Richardson number. By analysing long-time similarity solutions of the model, we find that the decrease in entrainment coefficient at large Richardson number, due to the suppression of turbulent mixing by stable stratification, qualitatively affects the structure and growth rate of the solutions, compared to currents in which the entrainment is taken to be constant or negligible. In particular, mixing is most significant close to the front of the currents, leading to flows that are more dilute, deeper and slower than their non-entraining counterparts. The long-time solution of an inviscid entraining gravity current generated by a lock-release of dense fluid is a similarity solution of the second kind, in which the current grows as a power of time that is dependent on the form of the entrainment law. With an entrainment law that fits the experimental measurements well, the length of currents in this entraining inviscid regime grows with time approximately as ${t}^{0. 447} $. For currents instigated by a constant buoyancy flux, a different solution structure exists in which the current length grows as ${t}^{4/ 5} $. In both cases, entrainment is most significant close to the current front.

scholarly journals Stratified gravity currents in porous media

2016 ◽  
Vol 791 ◽  
pp. 329-357 ◽  
Author(s):  
Samuel S. Pegler ◽  
Herbert E. Huppert ◽  
Jerome A. Neufeld
Keyword(s):  
Porous Media ◽  
Density Distribution ◽  
Vertical Structure ◽  
Gravity Current ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Density Field ◽  
Vertical Position ◽  
Uniform Density ◽  
Convex Shape

We consider theoretically and experimentally the propagation in porous media of variable-density gravity currents containing a stably stratified density field, with most previous studies of gravity currents having focused on cases of uniform density. New thin-layer equations are developed to describe stably stratified fluid flows in which the density field is materially advected with the flow. Similarity solutions describing both the fixed-volume release of a distributed density stratification and the continuous input of fluid containing a distribution of densities are obtained. The results indicate that the density distribution of the stratification significantly influences the vertical structure of the gravity current. When more mass is distributed into lighter densities, it is found that the shape of the current changes from the convex shape familiar from studies of the uniform-density case to a concave shape in which lighter fluid accumulates primarily vertically above the origin of the current. For a constant-volume release, the density contours stratify horizontally, a simplification which is used to develop analytical solutions. For currents introduced continuously, the horizontal velocity varies with vertical position, a feature which does not apply to uniform-density gravity currents in porous media. Despite significant effects on vertical structure, the density distribution has almost no effect on overall horizontal propagation, for a given total mass. Good agreement with data from a laboratory study confirms the predictions of the model.

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