A previously unreported shock feature associated with the scouring of a horizontal granular bed by a dam-break wave is discussed. Near the wave centre, the present study shows, the free surface breaks backward and a hydraulic jump forms. This behaviour is described from the standpoint of shallow-water theory, suitably extended to deal with non-equilibrium sediment transport. The shock formation involves a particularly strong coupling between flow free-surface evolution and bed morphodynamics. Support for our conclusions is sought through experimental and numerical approaches. In order to magnify the observed phenomena, measurements were performed for the case of light bed particles moving in sheet and debris flow modes. A detailed picture of the transient two-phase flow is presented, based on whole field acquisition of the grain motions by particle tracking techniques. Corresponding shallow-water solutions are constructed numerically using a shock capturing scheme. Finally, an interpretation of the jump formation is proposed based on the theory of characteristics.

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A set of digital imaging methods derived from the Voronoõ È diagram is proposed and tested on various liquid±granular ¯ow applications. The methods include a novel pattern-based particle-tracking algorithm, as well as estimators of the three-dimensional granular concentration from two-dimensional images. The proposed algorithms are able to resolve individual grain motions even for rapid shear ¯ows involving dense, ¯uctuating granular ensembles. Full automation is achieved, allowing the derivation of accurate statistics from large sets of individual measurements, as well as the construction of complete sets of grain trajectories. Results are presented for different applications: homogeneous ¯uidization, steady uniform debris ¯ow, and unsteady debris surges.

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Mathematical solutions are obtained for several sedimentary problems featuring semi-infinite alluvial channels evolving under diffusional sediment transport. Moving boundaries are considered at one end of the channels, and represent transitions between alluvial reaches and either bedrock-floored channels or bodies of standing water. Three elementary cases are considered: bedrock-alluvial transitions, lake breaches, and prograding deltas. It is shown that idealized formulations of all three problems share the same mathematical structure and admit exact similarity solutions. Elementary solutions can further be assembled to describe composite profiles. This is illustrated by the case of a natural lake undergoing simultaneous breaching and backfill. For both elementary and composite cases, the explicit solutions clarify the link between alluvial profile evolution and the migration of channel boundaries. For the case of lake breaching, for instance, the outlet channel profile is controlled simultaneously by downwards incision and upstream migration of the channel head. The pace of the resulting water-level drawdown in turn affects the form of the backfill deposits upstream of the lake.

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