Comparing lubrication approximation with shallow water equations for viscoplastic flows

A formal comparative numerical study of the lubrication approximation and the shallow water equations (SWE) for three-dimensional Herschel–Bulkley viscoplastic flows is presented. The validity limits and predictive capabilities of these models are compared across various flow regimes, i.e., in terms of the aspect ratio, inclination angle, rheological properties, basal slipperiness, and Reynolds, Froude, and Bingham numbers. The models’ abilities to capture flow deflections around obstructions are also evaluated. For validation, both model solutions are compared to dam-break experiments. In contrast to some previous works in the literature, both models are shown to adequately reproduce the experimental data in the low Reynolds number regime. The key difference arises during the early phase of a dam-break, where local Froude numbers are high, with the lubrication approximation appearing to overestimate front positions, whereas the SWE solutions align more closely with experimental observations. Furthermore, SWE provides better predictions of flow perturbations caused by obstructions and basal slipperiness. Overall, due to the inclusion of inertial effects, the present SWE model demonstrates broader predictive capability for viscoplastic flow dynamics than the lubrication approximation. However, both models converge as the inclination, aspect ratio, local perturbations, Froude and Reynolds numbers decrease, and as the Bingham number increases. • The accuracy of the lubrication (LA) and shallow water approximations (SWA) for viscoplastic flows is compared. • For the test cases considered the LA is shown to be remarkably robust despite neglecting inertia. • The LA fails to predict the early-stage flow dynamics, pronounced topographical, or trans-critical effects.