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.