We investigate the dynamics of a gravity current that propagates along the interface of a two-layer fluid. The results of the well-studied symmetric case are reproduced in which the upper-and lower-layer depth of the ambient are equal and the density of the intrusion is the average density of the ambient. In addition, we present the first detailed examination of asymmetric circumstances in which the density of the intrusion differs from the mean density of the ambient and in which the upper-and lower-layer fluid depths are unequal. The general equations derived by J. Y. Holyer & H. E. Huppert (J. Fluid Mech. vol. 100, 1980, pp. 739-767,), which predict the speed and vertical extent of the gravity current head, are re-expressed in a simpler form that employs the Boussinesq approximation. Approximate analytic solutions are determined using perturbation theory. The predictions are compared with the results of laboratory experiments. We find excellent agreement if the density of the gravity current is the average of the upper-and lower-layer densities weighted by the respective depths of the two layers. However, exact theory significantly underpredicts the gravity current speeds if the current density differs from this weighted-mean average. The discrepancy is attributed to the generation of waves that lead and trail the gravity current head. Empirical support for this assertion is provided through an examination of the observed wave characteristics.
We examine the response of a two- and three-layer salt-stratified fluid to the collapse of a mixed region intruding along the middle layer. For sufficiently deep middle layers, the intrusion (an interfacial gravity current) excites a double-humped solitary wave appearing in the interfacial layer in front of the intrusion head. When the solitary wave is generated the current stops propagating. Trailing the intrusion are large-amplitude trapped internal waves. We study the effect of middle-layer depth and density difference to determine the conditions under which a solitary wave is generated. We propose that this transition occurs because the intrusion resonantly couples with trapped internal waves for a sufficiently thick interface.
We present an experimental study of an axisymmetric turbulent fountain in a two-layer stratified environment. Interacting with the interface, the fountain is observed to exhibit three regimes of flow. It may penetrate the interface, but nonetheless return to the source where it spreads as a radially propagating gravity current; the return flow may be trapped at the interface where it spreads as a radially propagating intrusion or it may do both. These regimes have been classified using empirically determined regime parameters which govern the relative initial momentum of the fountain and the relative density difference of the fountain and the ambient fluid. The maximum vertical distance travelled by the fountain in a two-layer fluid has been theoretically determined by extending the theory developed for fountains in a homogeneous environment. The theory compares favourably with experimental measurements. We have also developed a theory to analyse the initial speeds of the resulting radial currents. The spreading currents exhibited two different flow regimes: a constant-velocity regime and an inertia-buoyancy regime in which the front position, R, scales with time, t, as R ∼ t3/4. These regimes were classified using a critical Froude number which characterized the competing effects of momentum and buoyancy in the currents.
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