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.