Two-dimensional two-layer model for dam-break induced geomorphic flows

Dam-break induced waves over mobile beds often generate significant sediment transport that can induce considerable morphological evolution leading to major risks for the surrounding population. To predict and mitigate the dramatic morphological consequences of these fast transient flows, the physical process underlying the sediment transport has to be described with special care. The proposed two-dimensional (2D) two-layer shallow-water description considers an upper layer made of clear water and a lower layer, called the bedload transport layer, made of a dense mixture of water and moving grains. These layers lay on a fixed bed and present distinct depth-averaged velocities [1]. The continuity and the 2D momentum conservation are written for each layer. The model accounts for the grain entrainment across the bed interface and for the mass and momentum exchanges between the flowing layers thanks to the definition of an erosion rate, itself depending on the shear stresses on both sides of the interfaces. The shear stresses are driven by Chezy-like closure equations. The assumption of distinct depth-averaged granular concentration in the mixture layer and the bed allows the required dilatancy of the mixture layer to be mobilised. The 7 7 system of governing equations, written in such a way that no loss of hyperbolicity occurs [2], is solved by a finite-volume scheme on an unstructured triangular mesh. An approximate Riemann solver derived from the Harten-Lax-Van Leer formalism is used. The numerical model is tested against three small-scale laboratory tests of dam-break induced flows over mobile beds: (1) subjected to a 1D morphological evolution [3], (2) a wave expansion on a floodplain and (3) in a channel featuring a sudden and non-symmetrical enlargement [4]. By comparison with the experimental measurements, the capability of the model to treat these fast transient flows is analysed