Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

Abstract

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.