Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

TLDR

Gravity currents in a two‑layer fluid exhibit an initial adjustment phase followed by a self‑similar inviscid phase with front speed decreasing as t⁻¹/³ when viscous effects are negligible. The study aimed to investigate the inviscid dynamics of gravity currents by conducting laboratory releases of a heavy fluid into a lighter fluid. Experiments were performed in a rectangular channel using salt water and fresh water, and the measured front depth, speed, and phase duration were compared with shallow‑water numerical solutions. The front remains steady during the initial phase and transitions to the self‑similar phase when a disturbance from the endwall overtakes it; the disturbance is an internal hydraulic drop when the heavy fluid depth is near the total depth, otherwise a long depression wave, and the phase duration, speed, and depth vary with the depth ratio.

Abstract

Results of laboratory experiments are presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density. The experiments were performed in a channel of rectangular cross-section, and the two fluids used were salt water and fresh water. As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases: an initial adjustment phase, during which the initial conditions are important, and an eventual self-similar phase, in which the front speed decreases as t−1/3 (where t is the time measured from release). The experiments reported herein were designed to emphasize the inviscid motion. From our observations we argue that the current front moves steadily in the first phase, and that the transition to the inviscid self-similar phase occurs when a disturbance generated at the endwall (or plane of symmetry) overtakes the front. If the initial depth of the heavy fluid is equal to or slightly less than the total depth of the fluid in the channel, the disturbance has the appearance of an internal hydraulic drop. Otherwise, the disturbance is a long wave of depression. Measurements of the duration of the initial phase and of the speed and depth of the front during this phase are presented as functions of the ratio of the initial heavy fluid depth to the total fluid depth. These measurements are compared with numerical solutions of the shallow-water equations for a two-layer fluid.