A Modelling Study of Transient, Buoyancy-Driven Exchange Flow over a Descending Barrier

Abstract

Results are presented from a series of model studies of the transient exchange flow resulting from the steady descent of an impermeable barrier separating initially-quiescent fresh and saline water bodies having density ρ0 and ρ0+(Δρ)0, respectively. A set of parametric laboratory experiments has been carried out (i) to determine the characteristic features of the time-dependent exchange flow over the barrier crest and (ii) to quantify the temporal increase in the thickness and spatial extent of the brackish water reservoir formed behind the barrier by the outflowing, partly-mixed saline water. The results of the laboratory experiments have been compared with the predictions of a theoretical model adapted from the steady, so-called maximal exchange flow case and good qualitative agreement between theory and experiment has been demonstrated. The comparisons indicate that head losses of between 7% and 3% are applicable to the flow over the ridge crest in the early and late stages, respectively, of the barrier descent phase, with these losses being attributed to mixing processes associated with the counterflowing layers of fresh and saline water in the vicinity of the ridge crest. The experimental data show (and the theoretical model predictions confirm) that (i) the dimensionless time of detection t det(g′/H b)1/2 of the brackish water pool fed by the dense outflow increases (at a given distance from the barrier) with increasing values of the descent rate parameter g'H b/(dh b/dt)2 and (ii) the normalised thickness δ(x,t)/H b of the pool at a given reference station increases monotonically with increasing values of the modified time (t−t det)/(H b/g′)1/2, with the rate of thickening decreasing with increasing values of the descent rate parameter g'H b(dh b/dt)2. Here, g′=(g/ρ0)(Δρ)0 is the modified gravitational acceleration, H b is the mean depth of the water and dh b/dt denotes the rate of descent of the barrier height h b with elapsed time t after the two water bodies are first brought into contact.