The slumping of gravity currents

Abstract

Experimental results for the release of a fixed volume of one homogeneous fluid into another of slightly different density are presented. From these results and those obtained by previous experiments, it is argued that the resulting gravity current can pass through three states. There is first a slumping phase, during which the current is retarded by the counterflow in the fluid into which it is issuing. The current remains in this slumping phase until the depth ratio of current to intruded fluid is reduced to less than about 0.075. This may be followed by a (previously investigated) purely inertial phase, wherein the buoyancy force of the intruding fluid is balanced by the inertial force. Motion in the surrounding fluid plays a negligible role in this phase. There then follows a viscous phase, wherein the buoyancy force is balanced by viscous forces. It is argued and confirmed by experiment that the inertial phase is absent if viscous effects become important before the slumping phase has been completed. Relationships between spreading distance and time for each phase are obtained for all three phases for both two-dimensional and axisymmetric geometries. Some consequences of the retardation of the gravity current during the slumping phase are discussed.

Dynamics of the head of gravity currents

“…Gravity currents have been widely studied in laboratory through both continuous ( [12,15,20,22,23,48] among many others) and instantaneous [2,25,29,36] releases of a heavier fluid into other fluid of lower density. Unsteady gravity currents experiments are usually performed through the lock-exchange technique [6,26,29,53,63], which consists in the release of a fixed volume of dense fluid into a lower density fluid.…”

“…Unsteady gravity currents experiments are usually performed through the lock-exchange technique [6,26,29,53,63], which consists in the release of a fixed volume of dense fluid into a lower density fluid. The differences in hydrostatic pressure between contacting fluids cause the denser fluid to flow along the bottom of the tank, while the lighter fluid flows along the top boundary, in the opposite direction.…”

Physical and numerical analysis of the front of a gravity current on a horizontal bottom

“…Th e analysis proposed by Hupper t a nd Simpson (1980) is based on two-dimensional spreading of a finite volume of a dense fluid. Initi a ll y, the height of the dense fluid is equal to the height of th e wa ter (H ).…”

Suspension-Driven gravity surges on horizontal surfaces: Effect of the initial shape

“…1 for schematics of the planar and cylindrical releases). These canonical setups have been extensively researched [14,16,[18][19][20][21][22]24,27] resulting in the development of a wide range of simple yet robust models. Indeed, one of the advantages of dealing with a simple geometric configuration is that at times the dimensional space may be reduced to two or even a single dimension making the derivation of elegant theoretical solutions possible.…”

“…Along with the box model [16] , the shallow water equations form a powerful tool in the sense that they have the ability to produce simple algebraic scaling relations to predict certain key aspects of gravity currents. For example, the extent of the deposit of a suspension-driven gravity surge initially confined within a circular cylinder may be expressed in terms of the initial parameters: cylinder dimensions, particle settling velocity, and particle volume fraction [4] .…”