UC Santa Barbara

Internal bores, also know as internal hydraulic jumps, can develop from phenomena in both oceanic and atmospheric situations. Classical approaches handle these bores in cases when density differences between the two layers are large, and more sophisticated approaches can now predict the bore height and propagation velocity in certain cases when the two layers have similar densities. These two-layer models, which conserve mass separately in each layer while conserving momentum across both layers, can generate reasonable predictions for bore velocity if the up and downstream layer heights are known. Traditionally, these models have needed to make assumptions about restricting the energy loss to either the upper or lower layer, but these assumptions are made unnecessary by utilizing conservation of vorticity. Within this work we propose utilizing vorticity conservation to first close the system of equations; after doing so, the energy drop across the bore can be calculated analytically. If we then enforce conservation of energy a predicted downstream layer height for bores can be generated that fits our analytical assumptions. By using this method we compare these model predictions to two-dimensional direct numerical simulations and find that it is possible to predict bore velocity, geometry, and to a lesser extent downstream behavior based on initial conditions only.