J. zyxwvutsrq Fluid zyxwvutsrqpo Mech. zyxwvutsrq (1995), vol. 292, pp. 39-53 zyxwvuts Copyright zyxwvutsrq 0 1995 Cambridge University Press zyxwvut 39 Gravity current flow over obstacles By G. F. LANE-SERFF, L. M. BEAL AND T. D. HADFIELD Department of Oceanography, The University, Southampton, SO 17 1 BJ, UK (Received 30 June 1994 and in revised form 21 November 1994) When a gravity current meets an obstacle a proportion of the flow may continue over the obstacle while the rest is reflected back as a hydraulic jump. There are many examples of this type of flow, both in the natural and man-made environment (e.g. sea breezes meeting hills, dense gas and liquid releases meeting containment walls). Two- dimensional currents and obstacles, where the reflected jump is in the opposite direction to the incoming current, are examined by laboratory experiment and theoretical analysis. The investigation concentrates on the case of no net flow, so that there is a return flow in the (finite depth) upper layer. The theoretical analysis is based on shallow-water theory. Both a rigid lid and a free surface condition for the top of the upper layer are considered. The flow may be divided into several regions: the inflow conditions, the region around the hydraulic jump, the flow at the obstacle and the flow downstream of the obstacle. Both theoretical and empirical inflow conditions are examined; the jump conditions are based on assuming that the energy dissipation is confined to the lower layer; and the flow over the obstacle is described by hydraulic control theory. The predictions for the proportion of the flow that continues over the obstacle, the speed of the reflected jump and the depth of the reflected flow are compared with the laboratory experiments, and give reasonable agreement. A shallower upper layer (which must result in a faster return velocity in the upper layer) is found to have a significant effect, both on the initial incoming gravity current and on the proportion of the flow that continues over the obstacle. 1. Introduction Gravity (or density) currents are buoyancy-driven flows, and may be of relatively dense fluid along a lower boundary or light fluid on an upper boundary or surface. They occur both in the natural environment and in man-made situations. They include sea breezes, estuary outflows, turbidity currents and accidental dense gas releases. This type of flow is reviewed (and many further examples given) by Simpson (1982, 1987). When a gravity current meets an obstacle some of the fluid may flow over or around the obstacle while a hydraulic jump will be reflected. (Moving hydraulic jumps are commonly referred to as ‘bores’.) For general obstacles, or for simple ridges or slopes at some angle to the oncoming flow, the reflected jump will be complicated and three- dimensional even if the oncoming flow was two-dimensional. The relation between the angles of the barrier to the oncoming current and to the reflected jump are of some interest as they have implications for estuarine mixing and sediment reworking in the oceanographic context (Thorpe, Hall & Hunt 1983; Kneller et al. 1991; Edwards 1993). Here we limit ourselves to the consideration of two-dimensional flows, such as a sea breeze meeting a ridge parallel to the front, so that the reflected jump will be in the opposite direction to the oncoming flow. When sea breezes occur there is often a low inversion, which effectively puts a ‘lid’ on the circulation. The presence of a return