Gravity currents can be thought of as either finite in volume, such as the pyroclastic flow from a volcano eruption, or continuously supplied from a source, such as warm air leaving the open doorway of a house in winter.
Gravity currents may be simulated by the shallow water equations, with special dispensation for the leading edge which behaves as a discontinuity.
In the latter case, the fluid in the head is constantly replaced and the gravity current can therefore propagate, in theory, forever.
The head, which is the leading edge of the gravity current, is a region in which relatively large volumes of ambient fluid are displaced.
The flow displays billowing patterns known as Kelvin-Helmholtz instabilities, which form in the wake of the head and engulf ambient fluid into the tail: a process referred to as "entrainment".
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.
This refers to the flow spreading along walls on both sides and effectively keeping a constant width whilst it propagates.
Sloshing induces a lot of mixing between the ambient and the current and this forms an accumulation of lighter fluid against the obstacle.
[7] Observations of intrusions and collisions between fluids of differing density were made well before T. B. Benjamin's study, see for example those by Ellison and Tuner,[8] by M. B. Abbot[9] or D. I. H.
[10] J. E. Simpson from the Department of Applied Mathematics and Theoretical Physics of Cambridge University in the UK carried out longstanding research on gravity currents and issued a multitude of papers on the subject.
He published an article[11] in 1982 for Annual Review of Fluid Mechanics which summarizes the state of research in the domain of gravity currents at the time.
There are also gravity currents with large density variations - the so-called low Mach number compressible flows.
Here, the dynamics of the problem are greatly simplified (i.e. the forces controlling the flow are not direct considered, only their effects) and typically reduce to a condition dictating the motion of the front via a Froude number and an equation stating the global conservation of mass, i.e. for a 2D problem where Fr is the Froude number, uf is the speed at the front, g′ is the reduced gravity, h is the height of the box, l is the length of the box and Q is the volume per unit width.
The front condition (Froude number) generally cannot be determined analytically but can instead be found from experiment or observation of natural phenomena.
The Froude number is not necessarily a constant, and may depend on the height of the flow in when this is comparable to the depth of overlying fluid.