Internal bores in two-layer exchange flows over sills

Internal bores are a common feature of tidally modulated two-layer exchange flows through straits and over sills. Even where the forcing changes smoothly, the flow may adjust with sudden jumps in the position of the interface between the two layers. The resulting flow configuration, with a hydraulically controlled exchange flow (at the sill) coupled with a propagating internal hydraulic jump (known as a bore), is investigated with mathematical models and laboratory experiments. The study concentrates on two-dimensional flow in a rectangular channel with a sill. The parameters considered are the depth of the channel compared to the depth over the sill, the depth of the interface before the passage of the bore and the strength of the net flux through the channel.The theory is based on shallow water equations and hydraulic control theory and includes the effects of a steady net flow through the channel (driven, for example, by the tide). Once the depth of the channel is twice the depth over the sill, further changes in geometry have relatively little effect on the flow. The bore velocity and fluxes are strongly affected by the strength of any net flow. The laboratory experiments model pure exchange flows (with no net flow) and give detailed information about the bores themselves. In many cases an undular bore is produced, with a well-defined wave train on the interface behind the front of the bore. The wavelengths and amplitudes of these internal waves are quantified and a brief comparison with similar internal waves observed in the Strait of Gibraltar is presented.