When two fluids of differing densities interact in such a way that a vertical
interface exists between the fluids, the resulting motion consists of the
heavier fluid flowing horizontally beneath the lighter fluid. Such a flow is
said to form a gravity current.
Gravity currents are widespread in nature, and their common characteristics are
observable in avalanches, heavy gas releases, turbidity currents, fresh and
salt-water exchange, and sea breezes. An excellent review of the nature of
gravity currents exists in the book by John Simpson, Gravity Currents in the
Environment and Laboratory (Cambridge University Press, 1997.)
One of the important factors which contribute to the structure of a gravity
current is the topography over which the current flows. Although a horizontal
surface is the ideal case to study, such a situation is usually the exception
rather than the rule in most physical applications. In a series of experiments
in 1966, G. V. Middleton noted that in general, gravity currents flowing over
small slopes (up to about 3.5 degrees) have similar properties to those flowing
over horizontal surfaces. He also further quantified previously known
results, stating that the front of the gravity current moves with a speed
that is proportional to the height at the front of the gravity current, and a
specific ratio of the density differences between the two fluids concerned.
Aim:
This experiment is designed to study the influence of bottom
topography on a propagating gravity current. It is limited to gravity currents
created by instantaneous volume releases in a finite rectangular tank.
Experimental Set-up:
A large rectangular tank was used to created the gravity currents, with the
following dimensions: 198 cm long, 17.5 cm wide, greater than 30 cm high. At
one end of the tank, a plexiglass plate could be inserted vertically at
diferrent locations, thus partitioning the tank into two sections. For the
purposes of this experiment, only two positions were used: the left and right
positions at 8.5 cm and 18.5 cm, respectively, from the end of the tank.
With the tank filled (up to a height of approximately 18 cm) with water and
partitioned, salt was added to the smaller section at the left, giving that
section a greater density than the tap water to the right. Lifting the
partition thus created a gravity current propagating the the right along the
bottom of the tank. To view this current, dye was injected into the salt
(heavy)
water. With a fluorescent light behind the tank, and a 5cm by 5cm grid drawn
on the side, the entire flow was recorded on tape to be played back and
analysed quantitatively later.
The problem of changing the slope of the bottom was overcome by placing foam
plastic wedges of varying thickness underneath the tank, thus elevating one end
while providing support at points along the tank's length. With the camera
tilted appropriately at a similar angle to the tank, the analysis of the
recording was simplified.
Experimental Procedure:
1. Insert lock and fill the tank with water.
2. Add salt and dye behind the insert, stir, and measure the density via
optical density measurement.
3. Start the camera, and remove the lock.
Results:
Four experiments were conducted, from which captured images from the video
recording are displayed below. Experiments 1 and 2 were initiated using
similar densities from the left lock position, with the major difference that
the tank was horizontal in Experiment 1 and inclined at 1.4 degrees in
Experiment 2. Experiment 3 was conducted with the same slope and with a
similar density difference as in Experiment 2, but with a larger volume gravity
current created by using the right lock position.
The recording of the experiments allowed quantitative results to be obtained
through use of the "digimage" program. Although these results are not
displayed here, as they require some interpretation, quick calculations did
produce results which were commensurate with Middleton's 1966 findings.
Several qualitative observations are listed below the gravity current pictures.
Some qualitative observations made during the experiments were:
1. The gravity current velocity increased with both volume of initial release
and density difference between the fluids.
2. The experiments initiated at the left lock position (lower volume gravity
currents) showed a slowing down of the gravity current in the later stages of
flow. This was not observed in the large volume gravity current experiments,
and is likely due to the increased importance of viscous effects as the gravity
current thins.
3. Less diffusion at the interface was apparent in the experiments with a
larger density difference.
4. The slope did not have a large effect on the form of the gravity current,
although the speeds were typically higher in the experiments with nonzero
slope.
5. The gravity current reflected at the wall, returning with a similar speed
after reflection.
6. The front height was approximately twice the height of the following
flow.
7. Interference by the bottom and side walls was slight unless the gravity
current became thin (less than a couple of cm).
8. The gravity current was not steady - the following flow was seen to be
moving faster than the front by observing small dirt particles in the fluid.
