The study of multilayered shallow water equations has developed from a consideration of immiscible layers as a vertical mesh to the layer bounds as imaginary extremes for vertical integration of the flow equations. In the current work, a quasi three-dimensional flow model has been developed with the consideration of the spatiotemporal flexibility/variability of the pervious vertical discretization/layer ratios. Thus, in principle, vertical layering offers a nonuniform grid with a temporal variation. The system of equations thus formulated comprises a conservative part and the appended source/sink terms. These source/sink terms pertain to the inter-layer interactions such as mass/momenta transfer and interfacial stress, which have been treated in a novel implicit form alongwith the subgrid-scale eddy-viscosity for interlayer shear. They are integrated into the system through different physical considerations so as to arrive at a well-balanced numerical scheme in a regular finite volume grid. The model has been validated through the standard test-cases highlighting the conservation properties and the model's adaptability to uniform and nonuniform vertical meshes alongwith the spatiotemporal transitions of layer ratios, with a specific interest in limiting cases of wet/dry fronts. The increase in layer ratios tends to nearly replicate the full-scale model results in experimental scenarios at a lesser computational overhead.

中文翻译：

---

分层浅水方程：时空变化的层比以及对湿/干界面的特定适应

多层浅水方程的研究已经从将不混溶层视为垂直网格发展到将层边界视为流动方程垂直积分的假想极值。在当前的工作中，考虑到渗透垂直离散/层比率的时空灵活性/可变性，开发了准三维流动模型。因此，原则上，垂直分层提供了具有时间变化的不均匀网格。由此制定的方程组包括保守部分和附加的源/汇项。这些源/汇项涉及层间相互作用，例如质量/动量传递和界面应力，它们已与层间剪切的亚网格尺度涡粘性一起以新颖的隐式形式进行处理。它们通过不同的物理考虑被集成到系统中，以便在规则的有限体积网格中达到良好平衡的数值方案。该模型已通过标准测试用例进行了验证，突出了保护特性以及模型对均匀和非均匀垂直网格以及层比时空转换的适应性，特别关注限制湿/干锋的情况。层比率的增加往往以较小的计算开销几乎复制实验场景中的全尺寸模型结果。