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Shallow water equations (SWEs) have been traditionally derived by integrating fundamental flow equations over a flow profile above a single point in a horizontal or nearly horizontal plane, with the main assumptions that the profile thickness is much smaller than other two dimensions and it contains only water. This paper presents the derivation of generalized SWEs (GSWEs) obtained for a finite plan area, allowing for the presence of phases other than water, such as air, grains, vegetation, and debris, which can be either stationary or mobile. The derivation provides a rigorous basis for various applications of layer-averaged models and opens numerous research questions, some of which are highlighted in the paper.

General shallow water equations (GSWEs)