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.

中文翻译：

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气腔双向传播的实验与数值模拟

这项研究通过数值和实验研究了与所谓的本杰明气泡相关的瞬态流动，但与以前的研究相比，该方法允许双向流动。两个实验研究了方形水箱中空气腔的双向传播；还使用三维数值模型模拟了这两个事件。采用完全保守的半拉格朗日格式来求解动量方程中的对流项和流体函数体积的对流方程。该模型与之前的一维 Benjamin 气泡实验数据和一维 Boussinesq 模型进行了比较。对于一维本杰明气泡实验，三维模型与已发表的数据和一维非流体静力模型均显示出良好的一致性。在对一维腔的推进进行建模后，使用三维模型模拟了双向本杰明气泡。数值结果与自由表面和加压区域的观察结果合理一致，并合理地预测了空气 - 水界面的形状。