Hydrodynamics of Gravity Currents Down a Ramp in Linearly Stratified Environments

Abstract

Gravity currents play an important role in many aspects of natural processes and engineering practice. This paper presents a systematic lock-exchange experimental study to investigate the influence of linearly stratified environments and ramp slope on the hydrodynamics of gravity currents. A high-speed camcorder and particle image velocimetry (PIV) are applied to analyze the macro- and microstructures of gravity currents. It is observed that the front velocity of the gravity currents increases first then decreases for both stratified and unstratified environments. However, the density contrast that drives the currents decreases more quickly in stratified environments as the currents descend the ramp, causing more intense deceleration of the front velocity, which indicates the damping of ambient stratification on gravity currents. Based on the thermal theory, a new set of analytical formulas is then developed to determine the front location and velocity at the deceleration stage by considering the ambient density variation at depth. Further downstream, the currents would separate from the ramp and then horizontally intrude into the ambience where the currents are neutrally buoyant if the relative stratification parameter S>1. An improved equation taking into account of the ramp slope, ambient stratification, and inflow buoyancy flux is proposed to predict the separation depth where the horizontal intrusion happens. Furthermore, velocity profiles in the body part of gravity currents are well predicted by two equations with three fitted parameters obtained by using the present experimental data. The vorticity fields of the gravity currents are quantitatively investigated to show that the weaker stratified ambience can lead to a stronger vorticity field, in which the Kelvin-Helmholtz instabilities and turbulent billows at the interface significantly affect the entrainment and mixing. In comparison with the gravity currents in the unstratified ambiance, the turbulent mixing in the stratified environments is generally reduced. The presence of stratification can result in a more complicated motion and fluid structure of the gravity currents.