Buoyancy-driven two-layer exchange flows across a slowly submerging barrier

Results are presented from a combined analytical and laboratory study of unsteady, two-layer, density-driven, sub-maximal exchange over a slowly-descending estuarine barrier located very close to the junction of the river mouth and the near-shore coastal zone. As in the precursor study (Cuthbertson et al. 2004, Environ. Fluid Mech. 4, 127-155) that the present investigation extends, the rate of descent of the barrier is assumed to be sufficiently slow for the unsteady exchange flow to adjust continuously to the appropriate quasi-steady conditions at every stage of the descent. The results demonstrate that the thickness of each layer at the barrier crest can be predicted satisfactorily by a hydraulic analysis that (i) assumes the existence of a single control point at the barrier crest and (ii) incorporates the hydraulic losses arising from the sudden expansion and contraction of the upper and lower layers, respectively, at the channel exit. Predictions of the normalised elevations of the interface at the barrier and exit for the "inviscid" maximal exchange case are shown to coincide with the maximal exchange predictions of Zhu and Lawrence.