Abstract
This study numerically and experimentally investigates the transient flow associated with a so-called Benjamin bubble, but, in contrast to previous studies, the approach permits bidirectional flow. Two experiments investigated the bidirectional propagation of an air cavity in a square tank; these two events were also simulated using a three-dimensional numerical model. An exactly conservative semi-Lagrangian scheme was employed to solve both the advection term in the momentum equation and the advection equation of the volume of fluid function. The model was compared with previous one-dimensional Benjamin bubble experimental data and a one-dimensional Boussinesq model. For the one-dimensional Benjamin bubble experiments, the three-dimensional model showed good agreement with both published data and a one-dimensional non-hydrostatic model. After modelling the advance of a one-dimensional cavity, a bidirectional Benjamin bubble was simulated using the three-dimensional model. The numerical results are in reasonable agreement with observations of the free surface and pressurized regions and reasonably predict the shape of the air–water interface.
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