This paper proposes an experimental study of the hydro- and morpho-dynamics induced by a slender vertical pile fitted into a sandy seabed and forced by sea waves in finite waters. The scour depth at the pile and the seabed morphology around it were measured and analyzed for both regular and random wave forcing. Scour depths due to regular waves were compared to those predicted in a previous study, revealing good agreement. The maximum scour depth occurred at the lateral side of the pile for waves characterized by a Keulegan-Carpenter (KC) number smaller than 7–8 and behind the pile for waves with KC > 7–8. Such a result revealed an asymmetric effect on the scour depth because of the weaker reversal flow. This behavior was more evident for nonlinear waves being crests larger than troughs and, as a consequence, vortices, responsible for the scour processes, became even more energetic around crest stages. To better understand the dynamics in front of, around, and behind the cylinder, pressure measurements were obtained to evaluate the generation and evolution of vortices. The pressure data showed that the adverse pressure gradient around the pile was higher than on the upstream of the pile. The analyses of the pressure data seemed to confirm that, if the forcing was only due to waves, the effect of the lee-wake vortices on the scour depth around the cylinder was stronger than that due to the horseshoe vortices. Finally, the practical stochastic method proposed by previous authors to compute the maximum scour depth around a vertical pile exposed to random waves was verified. The best adaptation between measured and predicted scour depths was obtained by taking into account approximately half of the highest waves (instead of one-tenth) over the threshold; such a condition is still cautionary for a practical point of view. A simplification of the previously discussed methodology was proposed in which the characteristic wave that generates the scour depth is defined.

The present study provides an extensive analysis on the hydrodynamics induced by a vertical slender pile under wave action. The authors carried out the study both experimentally and numerically, thus enabling a deep understanding of the flow physics. The experiments took place at a wave flume of the Università Politecnica delle Marche. Two different experimental campaigns were performed: In the former one, a mobile bed model was realized with the aims to study both the scour process and the hydrodynamics around the cylinder; in the latter one, the seabed was rigid in order to make undisturbed optical measurements, providing a deeper analysis of the hydrodynamics. The numerical investigation was made by performing a direct numerical simulation. A second order numerical discretization, both in time and in space, was used to solve the Navier–Stokes equations while a volume of fluid (VOF) approach was adopted for tracking the free surface. The comparison between experimental and numerical results is provided in terms of velocity, pressure distributions around the cylinder, and total force on it. The analysis of the pressure gradient was used to evaluate the generation and evolution of vortices around the cylinder. Finally, the relation between scour and bed shear stresses due to the structure of the vortex pattern around the pile was assessed. It is worth noting that the physical understanding of this last analysis was enabled by the combined use of experimental data on scour and numerical data on the flow pattern.

One single regular wave, traveling over a submerged abrupt discontinuity, can generate a pair of counter-rotating vortices. A nearbed vortex is generated by the flow separation that occurs at the bed, while a surface vortex can be generated by either a direct (co-rotating vortex) or a backward (counter-rotating vortex) breaking. Starting from recent laboratory test results, which highlighted the role of wave nonlinearity on the interaction between the counter-rotating vortices and led to the identification of three different regimes [Brocchini et al., “Interaction between breaking-induced vortices and near-bed structures: Part 1—Experimental and theoretical investigation,” J. Fluid Mech. 940, A44 (2022)], the present work illustrates the main findings obtained from the optical analysis of the flow field induced by three different wave conditions, each belonging to a specific nonlinear regime. For each test, the measured domain has been seeded with virtual particles to obtain long-lasting trajectories driven by the Eulerian flow field recovered through the particle tracking velocimetry analysis, to be studied by means of single-particle and multi-particle statistics. Both absolute and relative statistics confirm that a ballistic regime exists just after particle release (t≲TL) at each location of the domain. At times larger than the Lagrangian timescale (t≳TL), the absolute statistics suggest a sub-diffusive regime both within the vortices and between such areas (i.e., in correspondence of the breaking-induced jet), followed by a superdiffusive regime, dominated by rotation and particle release. Differently, the relative diffusivity suggests the occurrence of a superdiffusive regime at t≳TL, corresponding to an enstrophy cascade and exponential growth, followed by a Richardson regime and then by an oscillatory behavior, during which particles are periodically trapped and released by vortices.

The study of the scour around a monopile foundation and, in particular, the evaluation of the performance of alternative scour protection systems made of geotextile sand containers (GSCs) are here presented. Different configurations of the scour protection system were experimentally analyzed. The scour protection efficiency has been tested with both regular and random waves. A design dynamic formula for the scour protections is developed based on the stability of the GSC and, hence, on the evaluation of the weight of the geotextile sand container by means of the stability number. A damage level has been defined and related with the modified stability number. The paper provides useful information for the design of the scour protections made of geotextile sand containers, for the evaluation of the performance of such systems in terms of scour reduction, sinking and damage level of the scour protections.

The present work describes the vortex–vortex interactions observed during laboratory experiments, where a single regular water wave is allowed to travel over a discontinuous rigid bed promoting the generation of both near-bed and surface vortices. While near-bed vortices are generated by the flow separation occurring at the bed discontinuity, surface vortices are induced by the wave breaking in conjunction with a breaking-induced jet. A ‘backward breaking’ (previously observed in the case of solitary waves) occurs at the air–water interface downstream of the discontinuity and generates a surface anticlockwise vortex that interacts with the near-bed clockwise vortex. With the vortex–vortex interaction influenced by many physical mechanisms, a point-vortex model, by which vortices evolve under both self-advection (in relation to both free surface and seabed) and mutual interaction, has been implemented to separately investigate the vortex- and wave-induced dynamics. The available data indicate that both self-advection and mutual interaction are the governing mechanisms for the downward motion of the surface vortex, with the effect of the breaking-induced jet being negligible. The same two mechanisms, combined with the mean flow, are responsible for the almost horizontal and oscillating path of the near-bed vortex. The investigation of the vortex paths allow us to group the performed tests into three distinct classes, each characterized by a specific range of wave nonlinearity. The time evolution of the main variables characterizing the vortices (e.g. circulation, kinetic energy, enstrophy, radius) and their maximum values increase with the wave nonlinearity, such dependences being described by synthetic best-fit formulas.

The climate change process is leading to an increase in the sea level and the storm intensity. The associated shoreline recession can damage coastal facilities and also beaches protected by submerged/emerged breakwaters whose defense action can become ineffective. The application of cross-shore numerical models does not allow the performance of long-term analyses. In this paper, a semi-analytical model for the evaluation of shoreline recession due to waves and sea-level rise for free and protected beaches is proposed. The model is an extension of the Dean’s approach in which some limitations on the beach profile are overcome and the effects of breakwaters on the wave height (wave transmission) and on the water level (piling-up) are considered. The model takes into account a wide range of parameters for wave, sea level, beach profile, and breakwater characteristics. Among the breakwater parameters, the freeboard and the berm width are found to mainly affect the shoreline recession. For submerged breakwaters, an optimal value of the freeboard can be computed depending on the sea level and the offshore wave characteristics. The results of the model are then used to find prediction relations of the shoreline recession, with r² > 0.99, for both free and protected beaches, depending on the main hydrodynamic/geometrical characteristics.