Experiments on gravity currents propagating down slopes. Part 2. The evolution of a fixed volume of fluid released from closed locks into a long, open channel

Abstract

A series of experiments have been carried out on gravity currents released from locks of various dimensions into a sloping, open channel. Initially all the driving heads of the gravity currents grew by addition of heavier material from a following down-slope flow and by entrainment of ambient fluid, as in Maxworthy & Nokes (J. Fluid Mech., vol. 584, 2007, pp. 433–453). After propagating a distance of the order of 5–10 lock lengths the inflow into the rear stopped, and the head began to lose buoyancy-containing fluid from its rear by the detachment of large, weakly vortical structures. At the same time it was still entraining fluid over the majority of its surface so that its mean density was reduced. Measurements using a semi-direct method, in which dye concentration was used as a surrogate for density, have shown that the buoyancy in the current head increased during the first phase and decreased during the second. At no stage was the buoyancy constant except, of course, at the location and time at which the buoyancy was maximum with a magnitude significantly smaller than the initial value in the lock. Despite this the constant buoyancy theory of Beghin, Hopfinger & Britter (J. Fluid Mech., vol. 107, 1981, pp. 407–422), in which the head location x varies with time t as t2/3 during the later velocity-decay stage of the evolution, was found to be remarkably robust as a description of the evolution over both the latter part of the increasing-buoyancy stage and all of the decreasing-buoyancy phase. Critically, however, the multiplying coefficient had to be smaller than presented by them in order to track the experimental data with precision. This was due principally to the observation that the buoyancy at the beginning of the decay phase was considerably smaller than the initial buoyancy in the lock.