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The present work investigates the effect of the flow profile induced by an inlet condition on the roll-wave evolution in turbulent clear-water flows. The study employs theoretical and numerical analyses. Firstly, the influence of the inlet condition on the spatial evolution of a single perturbation in a hypercritical flow is examined through the expansion near a wavefront analysis. The results show that an accelerated unperturbed profile reduces the disturbance spatial growth. A decelerated profile causes an increase. The effect of the flow profile on the spatial evolution of roll-wave trains is then numerically investigated solving the Saint Venant equations with a second-order Runge-Kutta Total Variation Diminishing (TVD) Finite Volume scheme. The numerical simulations comply with the analytical results for the initial and transition phases of the roll-wave development. The unperturbed profile influences even the roll-waves statistical characteristics in the final stage, with a more evident effect in case of accelerated profiles. The influence of the flow profile should be therefore accounted for in the formulation of predictive criteria for roll-waves appearance based on the estimation of the disturbance spatial growth rate.

The paper addresses the prediction of roll-waves occurrence in mud-flows. The spatial growth of a point-wise disturbance is analytically described, based on the linearized flow model of a Herschel and Bulkley fluid, in the neighborhood of an initial uniform base condition. The theoretical achievements allow to generalize to mud-flows the minimum channel criterion commonly used for the prediction of roll-waves in clear-water. The applicability of the criterion is discussed through the comparison with literature laboratory data concerning unstable flows without rollwaves.

Dikes and levees are encountered very often along rivers. They are crucial as defence structures for flow channelization, protecting population and properties from floods as well as against lateral riverbed migration. However, the combination of their aging and increased exposition to extreme hydrological events may cause these structures to breach, and subsequently to fail. Understanding the dynamics of breaching is very important for developing adequate countermeasures, for civil protection initiatives and for land use planning. Recent literature shows many studies concerning, both from experimental and numerical point of views, frontal dike breaching. Based on several evidences, it is well assessed that depth-integrated numerical models can successfully reproduce this kind of phenomenon (e.g. Greco et al., 2012). Recently, Rifai et al. (2017) investigated a different setup in which the embankment is parallel to the main channel flow and thus a lateral breaching occurs. It is worth noting this scheme resembles real-world situation of levees breaching along a river. In present paper, the capability of depth-integrated approaches in reproducing such tests is investigated. Numerical results obtained with different models are compared against experiments from both the qualitative and quantitative point of views. Considerations about the applicability of depth-integrated models in real world situation of lateral breaching of dikes and levees are also drawn.