The slumping of gravity currents

TLDR

After the initial slumping, the gravity current enters a purely inertial phase where buoyancy balances inertia and surrounding fluid motion is negligible. The current first experiences a slumping phase retarded by counterflow until the depth ratio drops below about 0.075, after which it enters a viscous phase in which buoyancy is balanced by viscous forces. Experiments confirm that the gravity current passes through three distinct states—slumping, inertial, and viscous—and show that the inertial phase is absent when viscous effects dominate before slumping ends, with quantified spreading‑distance–time relationships for all phases in both 2D and axisymmetric geometries.

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.