Shallow Water Equations versus Zero-Inertia Approximation within a Geometrically Intrinsic Framework
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Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as mountain landscapes. In this work, we derive an intrinsic formulation for the diffusive wave approximation of the shallow water equations, defined on a local reference frame anchored on the bottom surface. We then derive a numerical discretization by means of a Galerkin finite element scheme intrinsically defined on the bottom surface. We aim to analyze the differences between the diffusive wave approximation and the shallow water model, both defined within a geometrically intrinsic framework and with a focus at the basin scale. Simulations on synthetic test cases show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures.
