Gravity Current - Propagation

Propagation

The leading edge moves at a Froude number of about 1; estimates of the exact value vary between about 0.7 and 1.4.

Gravity currents can originate either from finite releases or from constant releases. In the case of constant releases, the fluid in the head is constantly replaced and the gravity current can therefore propagate, in theory, for ever. In practice, constant releases could be encountered at river estuaries, where fresh water of low density encounters denser sea water and at high tide, the sea is pushing into the estuary. The sea water thereby constitutes a theoretically constant release gravity current. Of course, the tide will at some stage reverse and the gravity current thereby dissipate.

Most gravity currents will in fact occur as a result of a finite-volume release of fluid. In this case the propagation usually occurs in three phases. In the first phase the gravity current propagation is turbulent. The flow displays the billowing patterns described above and much mixing between the current and the environment can be expected. In this phase the propagation rate of the current is approximately constant with time.

As the driving fluid depletes as a result of the current spreading into the environment, the driving head decreases until the flow becomes laminar. In this phase, there is only very little mixing and the billowing structure of the flow disappears. From this phase onwards the propagation rate decreases with time and the current gradually slows down.

Finally, as the current spreads even further, it becomes so thin that viscous forces between the intruding fluid and the ambient and boundaries govern the flow. In this phases no more mixing occurs and the propagation rate slows down even more.

The spread of a gravity current depends on the boundary conditions, and two cases are usually distinguished depending on whether the initial release is of the same with as the environment or not.

In the case where the widths are the same, one obtains what is usually referred to as a "lock-exchange" or a "corridor" flow. This refers to the flow spreading along walls on both sides and effectively keeping a constant width whilst it propagates. In this case the flow is effectively two-dimensional. Experiments on variations of this flow have been made with lock-exchange flows propagating in narrowing/expanding environments. Effectively, a narrowing environment will result in the depth of the head increasing as the current advances and thereby its rate of propagation increasing with time, whilst in an expanding environment the opposite will occur.

In the other case, the flow spreads radially from the source forming an "axisymmetric" flow. The angle of spread depends on the release conditions. In the case of a point release, an extremely rare event in nature, the spread is perfectly axisymmetric, in all other cases the current will for a sector.

When a gravity encounters a solid boundary, it can either overcome the boundary, by flowing around or over it, or be reflected by it. The actual outcome of the collision depends primarily on the height and width of the obstacle. If the obstacle is shallow (part) of the gravity current will overcome the obstacle by flowing over it. Similarly, if the width of the obstacle is small, the gravity current will flow around it, just like a river flows around a boulder.

If the obstacle cannot be overcome, provided propagation is in the turbulent phase, the gravity current will first surge vertically up (or down depending on the density contrast) along the obstacle, a process known as "sloshing". Sloshing induces a lot of mixing between the ambient and the current and this forms an accumulation of lighter fluid against the obstacle. As more and more fluid accumulates against the obstacle, this starts to propagate in the opposite direction to the initial current, effectively resulting in a second gravity current flowing on top of the original gravity current. This reflection process is a common feature of doorway flows (see below), where a gravity current flows into a finite-size space. In this case the flow repeatedly collides with the end walls of the space, causing a series of currents travelling back and forth between opposite walls. This process has been described in details by Lane-Serf.