The impact of a dam-break wave on an erodible embankment with a steep slope is studied in the paper using both experimental and numerical approaches. The laboratory experiments have been specifically designed and performed for a range of the storage water levels and the embankment elevations and slopes. The simulations were carried out using a recently-developed two-phase depth-integrated model, supplemented with a geofailure operator to account for the possible occurrence of geotechnical collapses. A comparison between numerical and experimental results indicates that the two-phase model reproduces the experimental free surface elevation well, with or without the geofailure operator. On the other hand, especially for high embankment slopes, this operator appears to be important for predicting the observed morphological evolution. The results also show that, due to the geotechnical collapses, water and sediment velocities may have opposite signs. While the models based on equal direction of the liquid and the solid motions cannot reproduce this effect, the proposed two-phase approach easily accounts for such a peculiarity of the investigated process.

This paper numerically investigates the effects of a harmonic volume forcing of prescribed frequency on the turbulent pipe flow at a Reynolds number, based on bulk velocity and pipe diameter, of 5900. The thickness of the Stokes layer, resulting from the oscillatory flow component, is a small fraction of the pipe radius and therefore the associated vorticity is confined within a few wall units. The harmonic forcing term is prescribed so that the ratio of the oscillating to the mean bulk velocity ( $\ensuremath{\beta} $ ) ranges between 1 and 10.6. In all cases the oscillatory flow obeys the Stokes analytical velocity distribution while remarkable changes in the current component are observed. At intermediate values $\ensuremath{\beta} = 5$ , a relaminarization process occurs, while for $\ensuremath{\beta} = 10. 6$ , turbulence is affected so much by the harmonic forcing that the near-wall coherent structures, although not fully suppressed, are substantially weakened. The present study focuses on the analysis of the time- and space-averaged statistics of the first- and second-order moments, vorticity fluctuations and Reynolds stress budgets. Since the flow is unsteady not only locally but also in its space-averaged dynamics, it can be analysed using phase-averaged and time-averaged statistics. While the former gives information about the statistics of the fluctuations about the mean, the latter, postponed to a subsequent paper, shows how the mean is affected by the fluctuations. Clearly, the two phenomena are connected and both of them deserve investigation.

Fast geomorphic transients may involve complex scenarios of sediment transport, occurring near the bottom as bed load (i.e., saltating, sliding, and rolling) or as suspended load in the upper portion of the flow. The two sediment transport modalities may even coexist or alternate each other during the same event, especially when the shear stress varies considerably. Modeling these processes is therefore a challenging task, for which the usual representation of the flow as a mixture may result in being unsatisfactory. In the present paper, a new two-phase depth-averaged model is presented that accounts for variable sediment concentration in both bed and suspended loads. Distinct phase velocities are considered for bed load, whereas the slip velocity between the two phases is neglected in the suspended load. It is shown that the resulting two-phase model is hyperbolic, and the analytical expression of the eigenvalues is provided. The entrainment/deposition of sediment between the bottom and the bed load layer is based on a modified van Rijn transport parameter, whereas for the suspended sediment a first-order exchange law is considered. A numerical finite-volume method is used for the simulation of three dam break experiments found in the literature, which are effectively reproduced in terms of both free surface elevation and bottom deformation, confirming the key role played by the solid concentration variability even for two-phase models.

This paper is the follow-up of a previous study (Manna, Vacca & Verzicco,J. Fluid Mech., vol. 700, 2012, pp. 246–282) that numerically investigated the effects of a harmonic volume forcing on the turbulent pipe flow at a bulk Reynolds number of $\simeq 5900$ . There, the investigation was focused on the time- and space-averaged statistics of the first- and second-order moments of the velocity, the vorticity fluctuations and the Reynolds stress budgets in order to study the changes induced on the mean current by the oscillating component. The amplitude of the latter was used as a parameter for the analysis. However, as the flow is inherently unsteady, the phase-averaged statistics are also of interest, and this is the motivation and subject of the present study. Here, we show the variability of the above quantities during different phases of the flow cycle and how they are affected by the amplitude of the oscillation. It is observed that when the ratio of the oscillating to the time-constant velocity component is of the order of one ( ${\it\beta}\simeq O(1)$ ), the phase-averaged profiles are appreciably influenced by the pulsation, although only small deviations of the time-averaged counterparts have been documented. In contrast, when that ratio is increased by one order of magnitude ( ${\it\beta}\simeq O(10)$ ) the phase- and cycle-averaged quantities differ considerably, especially during the decelerating part of the cycle. In more detail, the amplitude and the phase of all turbulence statistics show significant variations with ${\it\beta}$ . This variability has important implications in the dynamics and modelling of these flows. Since the data have been obtained by direct numerical simulations and validated by comparisons with experimental studies, the results could be used for validation of codes, testing of turbulence models or measurement procedures.