John E. Simpson

The slumping of gravity currents

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 fluidinto 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. R’elationships 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.

Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

Results of laboratory experiments are presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density. The experiments were performed in a channel of rectangular cross-section, and the two fluids used were salt water and fresh water. As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases : an initial adjustment phase, during which the initial conditions are important, and an eventual self-similar phase, in which the front speed decreases as t-4 (where t is the time measured from release). The experiments reported herein were designed to emphasize the inviscid motion. From our observations we argue that the current front moves steadily in the first phase, and that the transition to the inviscid self-similar phase occurs when a disturbance generated at the endwall (or plane of symmetry) overtakes the front. If the initial depth of the heavy fluid is equal to or slightly less than the total depth of the fluid in the channel, the disturbance has the appearance of an internal hydraulic drop. Otherwise, the disturbance is a long wave of depression. Measurements of the duration of the initial phase and of the speed and depth of the front during this phase are presented as functions ofthe ratio of the initial heavy fluid depth to the total fluid depth. These measurements are compared with numerical solutions of the shallow-water equations for a two-layer fluid.

THE DYNAMICS OF THE HEAD OF A GRAVITY CURRENT ADVANCING OVER A HORIZONTAL SURFACE

The motion behind the head of a gravity current advancing over a no-slip horizontal surface is a complex three-dimensional flow. There is intense mixing between the current and its surroundings and the foremost part of the head is raised above the surface. Experimental results are obtained from (i) an apparatus in which the head is brought to rest by using an opposing flow and a moving floor and (ii) a modified lock exchange flow. The dimensionless velocity of advance, rate of mixing between the two fluids and the depth of the mixed layer left behind the head and above the following gravity current are determined for an extended range of the dimensionless gravity current depth. The mixing between the two fluids is the result of gravitational and shear instabilities at the gravity current head. A semi-empirical analysis is presented to describe the results. The influence of Reynolds number is discussed and comparison with a documented atmospheric flow is presented.

Experiments on the dynamics of a gravity current head

Some of the dense fluid at the front of an advancing gravity current is observed to be mixed with the ambient fluid. This process continues when the cross-stream non-uniformities at the head of the current are suppressed by advancing the floor beneath the head. In the resulting two-dimensional flow regular billows are visible. This paper considers experimentally and analytically the inviscid gravity current head and specifically includes the observed mixing at the head. Experimental results were obtained with an apparatus in which the head of the gravity current was brought to rest by an opposing uniform flow. The mixing appears to occur through Kelvin-Helmholtz billows generated on the front of the head and controls the dynamics of the head. A momentum balance is used to analyse the flow and the problem is closed by quantitatively introducing the billow structure.

Gravity-driven flows in a turbulent fluid

The formation and destruction of a gravity current in a turbulent fluid is examined in laboratory experiments. The gravity current is produced by lock exchange and the fluid is kept turbulent by bubbling air from the base of the tank. When the lock is released the buoyancy forces associated with the reduced gravity g ′ between the fluid on the two sides of the lock drives a counterflow, with the dense fluid slumping underneath the less-dense fluid, and a gravity current is formed. The current has a sharp density front at its leading edge, and a stable density stratification is established behind the front. The turbulence, characterized by a longitudinal turbulent diffusion coefficient K , tends to mix this stable stratification. Once the fluid is vertically mixed the gravity current front is destroyed, and the density varies smoothly with horizontal distance over a zone whose length increases with time owing to the continuing longitudinal turbulent diffusion and buoyancy driving. It is found that the gravity current propagates over a distance L 1 before it is destroyed, where L 1 / H ≈ 0.08( g′H ) ½ H/K , and H is the fluid depth. At this point turbulent dissipation balances the buoyancy driving and frontogenesis is inhibited. The turbulent dispersion coefficient is found to increase with the buoyancy driving with K ∞ Ri ½ , where Ri = g′H/q 2 and q is the r.m.s. turbulence velocity fluctuations. It is also shown that when the turbulence level is reduced nonlinearities in the horizontal density gradient can sharpen up to form a front. The implications of these frontogenetical processes to the sea-breeze front and fronts in shallow seas is discussed.

The propagation of a gravity current into a linearly stratified fluid

The constant initial speed of propagation ( V ) of heavy gravity currents, of density ρ C , released from behind a lock and along the bottom boundary of a tank containing a linearly stratified fluid has been measured experimentally and calculated numerically. The density difference, bottom to top, of the stratification is (ρ b −ρ 0 ) and its intrinsic frequency is N . For a given ratio of the depth of released fluid ( h ) to total depth ( H ) it has been found that the dimensionless internal Froude number, Fr = V / NH , is independent of the length of the lock and is a logarithmic function of a parameter R = (ρ C −ρ 0 )/(ρ b −ρ 0 ), except at small values of h/H and R close to unity. This parameter, R , is one possible measure of the relative strength of the current (ρ C −ρ 0 ) and stratification (ρ b −ρ 0 ). The distance propagated by the current before this constant velocity regime ended ( X tr ), scaled by h , has been found to be a unique function of Fr for all states tested. After this phase of the motion, for subcritical values of Fr , i.e. less than 1/π, internal wave interactions with the current resulted in an oscillation of the velocity of its leading edge. For supercritical values, velocity decay was monotonic for the geometries tested. A two-dimensional numerical model incorporating a no-slip bottom boundary condition has been found to agree with the experimental velocity magnitudes to within ±1:5%.

Unsteady gravity current flows over obstacles: some observations and analysis related to the phase II trials

Abstract The Phase II trials at Thorney Island were designed to provide a few full-scale results of the interaction of heavy gas clouds with surface-mounted obstacles. In this paper, we interpret some preliminary observations from the Phase II trials by reviewing and developing the theory of two-layer fluid flows over obstacles and comparing these results with visual observations of the field trials. The results are preliminary, and largely qualitative, because the concentration and other quantitative measurements are not yet available.

A note on the structure of the head of an intrusive gravity current

The head of an intrusive flow advancing along the interface between two fluids is studied experimentally when the two layers are of equal depth and the density of the intrusion is the mean of the two densities. The dependence of the flow on the interface thickness and the depth of the intrusion is determined. When the interface is very thin the flow is similar to the nominally inviscid gravity currents observed by Britter & Simpson (1978).

Vortical motion in the head of an axisymmetric gravity current

A series of experiments that examine the initial development of an axisymmetric gravity current have been carried out. The experiments highlight the growth of a ring vortex that dominates the dynamics of the gravity current’s early time propagation. In particular, the experiments show three distinct stages of early time development that have previously been described as the “initial phase” of a gravity current. The first phase of the early time development is dependent on the fractional depth of the lock release, followed by a secondary phase wherein the frontal speed is approximately constant and a third phase of reducing speed. The second phase of the gravity current’s propagation comes to an abrupt end with the breakdown of the ring vortex at a clearly defined position. All of the experimental results show the development of a complex flow field where the generation and collapse of a ring vortex dominate the gravity current’s early time propagation. The complexity of the flow field and the dependence of the propagation speed on the presence of the ring vortex in the head of the gravity current highlights the unsuitability of shallow-water modeling for axisymmetric lock releases at early times.

The Initial Development of Gravity Currents from Fixed Volume Releases of Heavy Fluids

This paper describes some laboratory experiments of the initial development of gravity currents resulting from the instantaneous release of a fixed-volume of one fluid into a cross flow of another fluid of lesser density. Two limiting cases are considered in detail: the release of a cylindrical volume of neutrally-buoyant fluid into a uniform cross flow and the release of a cylindrical volume of heavy fluid into still surroundings. The results of the experiments are interpreted in terms of simple models.