Gravity currents in two-layer stratified media

Abstract

An analytical, experimental and numerical study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. Gravity currents are supposed to originate from a lock-release apparatus; the (heavy) gravity current fluid is assumed to span the entire channel depth, H , at the initial instant. Our theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, and follows from the classical analysis of Benjamin (J Fluid Mech 31:209-248, 1968). In contrast to previous investigations, we argue that the interfacial disturbance must be parameterized so that its amplitude can be straightforwardly determined from the ambient layer depths. Our parameterization is based on sensible physical arguments; its accuracy is confirmed by comparison against experimental and numerical data. More generally, measured front speeds show positive agreement with analogue model predictions, which remain strictly single-valued. From experimental and numerical observations of supercritical gravity currents, it is noted that this front speed is essentially independent of the interfacial thickness, δ, even in the limiting case where δ = H so that the environment is comprised of a uniformly stratified ambient with no readily discernible upper or lower ambient layer. Conversely, when the gravity current is subcritical, there is a mild increase of front speed with δ. Our experiments also consider the horizontal distance, X , at which the front begins to decelerate. The variation of X with the interface thickness and the depths and densities of the ambient layers is discussed. For subcritical gravity currents, X may be as small as three lock lengths whereas with supercritical gravity currents, the gravity current may travel long distances at constant speed, particularly as the lower layer depth diminishes.

Gravity currents propagating up a slope in a two-layer fluid

“…Similar observations have been made previously in related laboratory experiments. 22,23,30,33 The measured interfacial disturbance amplitude compared well with the semi-empirical prediction of Tan et al, 19 albeit with a smaller value for the fitting parameter that relates the amplitude to the initial lock conditions. The half-width and speed of the interfacial disturbance were found to increase with amplitude.…”

“…The uniform advection and the abrupt halting of a gravity current head due to interactions with interfacial disturbances have been noted previously for horizontal gravity currents and intrusions in a two-layer ambient and in uniform stratification. 18,22,23,33…”

A general description of a gravity current front propagating in a two-layer stratified fluid

“…Tan et al (2011) also presented a steady theory for the gravity current front speed in a two-layer ambient, instead closing the problem with an ad hoc approximation to the interface displacement over the current,…”

Generation of internal solitary waves by frontally forced intrusions in geophysical flows

“…The generation of internal solitary waves by the gravitational collapse of mixed fluids is not limited to cases of surface (for example, river plumes) or bottom (for example, Morning Glory) density currents but may also arise, under some circumstances, from interfacial gravity currents or intrusions, in two-layer fluids, as reproduced in several lock-exchange laboratory experiments20212223242930. One important result of laboratory experiments is that large-amplitude internal solitary waves that are able to detach and lead the interfacial gravity current head are only generated when the initial motionless condition is said to be in non-equilibrium, that is, when the centre of mass of the lock water rises or falls when the gate is removed21222331.…”