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Abstract
A mathematical model is developed for a high Reynolds number, quasi-steady, intrusive gravity current propagating into a two-layer ambient fluid. The model is based on inviscid, irrotational flow theory, and is used to predict the rate of advance of the current front as a function of its head height. The key underlying assumptions of the model are that the local conditions at the head determine its speed of propagation, and that the upstream portion of the head is well approximated by an inviscid, irrotational flow. In order to provide a complete set of boundary conditions it is assumed that the ambient flow over the top of the head is horizontal, but not uniform. An upper bound solution is derived and is compared with a full solution generated with an optimisation based Boundary Element Method technique. The upper bound solution is shown to be entirely adequate for relative current heights greater than 0.3. The results from two experimental programmes provide support for the model predictions, and particle tracking velocimetry measurements indicate that the assumption of horizontal flow over the head is reasonable.