This paper concerns the second-gradient compressible fluids model and examines the mechanical constitutive equations that yield the Navier-Stokes equations with additional terms accounting for hyperviscosity effects via higher-order spatial derivatives of the velocity field. Some general aspects are reviewed, including the field equations governing momentum and kinetic energy, with particular attention paid to the definition and interpretation of pressure. The correspondence between the resulting field equations and the quasi-incompressible Reynolds-Averaged Navier-Stokes (RANS) equations is established. As a specific application with engineering relevance, the second-gradient model is employed to describe anomalously large viscous dissipation in the propagation of finite-amplitude pressure waves in water-filled pipes, a phenomenon commonly referred to as water hammer waves. Within a one-dimensional (1D) formulation, a wave equation is derived, highlighting the influence of a new dimensionless number that dimensional analysis identifies as crucial for wave propagation and kinetic energy dissipation. Phenomenological parameters are estimated by fitting the analytical solution of the wave equation (derived under appropriate initial and boundary conditions) to experimental data available in the literature. The accuracy of the 1D model is assessed, and its strengths, limitations, and critical aspects are discussed.

Overhanging parapets are commonly adopted in vertical breakwaters to reduce wave overtopping. However, previous studies have shown that these structures may also be subjected to significant impulsive loads associated with the Confined-Crest Impact (C-CI) phenomenon. While the loading mechanisms of conventional recurved parapets have been extensively investigated, the influence of alternative overhanging geometries on both wave loading and overtopping reduction remains poorly understood. This study investigates the hydraulic efficiency and wave loading on rectilinear, recurved, and recurved crownwall under non-breaking wave conditions by means of Reynolds-Averaged Navier-Stokes (RANS) simulations coupled with a Volume of Fluid (VOF) approach. The results show that parapet geometry strongly influences both dynamic/impulsive wave loading and overtopping volumes. The recurved crownwall achieves the greatest overtopping reduction but also the highest force amplification. Conversely, the recurved parapet produces the lowest impulsive loads among the tested overhanging geometries, at the expense of hydraulic efficiency, although these loads remain higher than those experienced by the reference vertical parapet. These findings reveal a trade-off between overtopping mitigation and structural loading, indicating that the most hydraulically effective geometry is not necessarily the most structurally advantageous.

Wave energy variability plays a crucial role both in characterizing wave-energy resources and in defining the wave climate of exposed coasts. On the one hand, the temporal variability of the resource is a key factor in assessing the economic viability of wave energy extraction projects. On the other hand, it is well known that the short-term morphodynamic response of sandy beaches is intimately related to the temporal succession of sea states. The aim of this manuscript is therefore to propose a simple method for the quantitative characterization of wave energy variability. The method relies on a synthetic variability index, based on the use of the Gini coefficient, aimed at quantifying the temporal concentration of wave energy. The method is applied to the case study of the Mediterranean and Black Seas in order to demonstrate its feasibility, applicability, and reliability. The results highlight that both wave energy availability and variability should be considered in the preliminary identification of suitable areas for wave energy exploitation and in the definition of coastal and offshore planning strategies.

This paper proposes the regional frequency analysis, bias correction and downscaling of ERA5-Land snow depth and increase of snow depth over three consecutive days, with the aim of quantifying design loads at ungauged sites and accurately assessing avalanche hazard. Local statistical analyses are typically performed by extracting extremes for snow depth time series. The latter are often incomplete, especially during extreme snowfall events. Furthermore, in most cases the stations are not found at elevations where avalanches typically release. In contrast, ERA5-Land provides broader spatial and temporal coverage, though it is affected by biases that lead to an under-or overestimation of extreme values. To address these limitations, a regional frequency analysis is proposed for both observed and ERA5-Land snow related variables. The adopted method is the index value regional method, which lead to the identification of homogeneous areas according to common snowfall and avalanche occurrence patterns. A bias correction and downscaling approach was then applied, based on a comparison between the cumulative distribution functions of regionalised observed and ERA5-Land variables for the area of Central Italy, taken as case study. Calibration values derived from this comparison were then used to adjust ERA5-Land quantiles, thus providing a simple procedure to extrapolate design loads at the local scale.

Wave overtopping represents a critical design issue for rubble-mound breakwaters, particularly in the current context of climate change. This study investigates the influence of submerged berms on overtopping phenomena at rubble mound breakwaters through an integrated experimental-numerical approach, considering its inclusion both in the design of new structures and in the upgrading of existing ones. Small-scale physical model tests have been conducted to qualitative validate the numerical model computations, providing insight into the response of overtopping discharges under varying sea states and berm configurations. A comprehensive parametric numerical investigation has been subsequently performed using IH2VOF numerical model, focusing on the effects of berm geometry. The model has been calibrated and validated to ensure an accurate representation of both water-surface elevation and overtopping phenomena. Within the tested range, the numerical results indicate that submerged berms systematically reduce overtopping discharges compared to conventional configurations without a berm, with enhanced effectiveness observed for increased berm height and length. Such effects have been synthesized into an empirical reduction parameter, formulated as a function of the dimensionless berm height and length, to be used within existing overtopping prediction methods developed for conventional structures. A comparison between modeled and predicted overtopping discharges demonstrates the reliability of the proposed formulation.

Wave overtopping is one of the main phenomena influencing the performance of harbor structures in protecting the sheltered area (EurOtop, 2018). Indeed, the configuration of such a kind of structure is often selected to limit the wave overtopping that could threaten the safety of activities performed in harbors (Buccino et al., 2023). Usually, the wave overtopping is quantified by referring to the mean overtopping rate, the individual wave overtopping volume, and the thickness and velocity of the overtopping jet (e.g. Schüttrumpf et al. 2002; Mares-Nasarre et al., 2019; Altomare et al., 2020). This work aims to propose a simple method to measure the instantaneous features of overtopping events. The method relies on the use of a specific experimental device designed to provide a semi-empirical model with the needed information to get the instantaneous overtopping discharge flowing at the crest of the investigated structure.

The prediction of sandy shoreline evolution, over both short/medium- and long-term temporal scales for small and large spatial scales, remains a challenge for coastal researchers and engineers. Basically, the configuration of sandy beaches, which are characterized by high complexity, are influenced by waves-sediment interaction. Coastal zones, which have a significant environmental, tourist, and economic value, are constantly exposed to natural (e.g., waves, tides, climate change) and human (e.g., over-exploitation by the construction of railways, roads, and private buildings close to the beach) pressures. One- line models, with a particular focus on the study of curved shorelines, and the development of coastal shoreline features, such as spits, cups, and rhythmic shoreline undulations (Ashton and Murray, 2006a, b; Kaergaard and Fredsoe, 2013a; Hurst et al., 2015; Robinet et al., 2018, 2020) have been developed. Other one-line models (Vitousek et al., 2017; Antolinez et al., 2019) have explored the impact of the cross-shore sediment transport on long- term shoreline dynamics, accounting not only for river inputs, beach nourishments, sand-bypassing (Pelnard- Considère, 1956), but also cross-shore transport due to wave action (Yates et al., 2009) and water level variation due to sea level rise (Bruun,1962), storm surge, and monthly sea level anomalies. In this context, the work described hereinafter is aimed to provide the scientific and technical communities with a comprehensive one-line tool, covering hydrodynamics and morphodynamics processes.

In the recent years, the effects of climate change are becoming increasingly evident (e.g., Naughten et al., 2023; Pörtner et al., 2022). Sea level rise, change in the intensity of storm surge, and wave heights are typical consequences of climate change in the coastal environment (e.g., Toimil et al., 2020). Therefore, coastal structures deployed to protect coastlines and harbors from wave action, may become ineffective due to the potential increase of wave loads, run-up, and overtopping phenomena (e.g., Galiatsatou et al., 2018). Indeed, several adaptation measures for existing coastal structures have been proposed (e.g., Burcharth et al., 2014). Past research studies illustrated how the deployment of a berm in the seaward side of conventional rubble mound breakwaters can significantly improve the performance of the structure. (e.g. Van Gent, 2013; Celli et al., 2018; Celli et al., 2021). Basically, the presence of a berm enhances the wave energy dissipation at the toe of the armor layer. Besides the stability of the structure, this could be effective in the reduction of wave run-up, and overtopping phenomena, potentially. To investigate the role of the submerged berm on the wave run-up phenomenon, a series of 2D experimental tests is being carried out at the Environmental and Maritime Hydraulic Laboratory (LIam) of the University of L'Aquila.

Future development must be linked to environmental sustainability and better resource utilization is one of the key points of global political guidelines. Indeed, the management and improvement of water quality is one of the 17 Sustainable Development Goals of the 2030 agenda. Therefore, exploring the evolution of released pollutants and contaminants poses a significant challenge in the fields of marine sciences and environmental hydraulics, with implications for both natural and industrial environments. Examples of potential release sources that could have a detrimental impact on the water quality include dredging operations, deep-sea mining, wastewater discharge in oceans or rivers, and unintended spills of pollutant substances.

The snow depth and the increase of snow depth after three consecutive days of snowfall, hereinafter referred to as ds and DH3gg, respectively, are typically chosen for avalanche protection and avalanche hazard assessment purposes. With specific reference to the Central Apennines (Central Italy), the preferable provider of observations for avalanche related applications is MeteoMont, which supplies ds observations at 34 manual stations, measured between 1978 and 2023. The area of interest is also covered by ERA5-Land, over a period of 73 years, from 1950 to 2023. In terms of temporal, spatial and quantitative availability of snow information, ERA5-Land consists in a more appealing choice as most manual weather stations set up in the Central Apennines are located at lower altitudes compared to where avalanches are likely to occur. Moreover, data recorded at manual stations appears to be incomplete, especially during extreme snowfall events. However, it is necessary to stress that ERA5-Land is affected by biases (e.g. underestimation or overestimation of extremes) and the use of uncorrected data in all applications might lead to unreasonable results. Therefore, in order to overcome the listed limitations, the suggested approach consists in the regionalisation of both ERA5-Land and MeteoMont ds and DH3gg and in the subsequent bias correction and downscaling of the regionalised ERA5-Land variables by means of the regionalised MeteoMont ones. With regards to ERA5-Land, 51 nodes have been considered as their grids intersect recorded and reconstructed avalanche paths in the Abruzzo Region (extracted from the Avalanche Record and the Map of Probabilistic Location of Avalanches provided by the Abruzzo Region). This ensures that the selected nodes are solely representative of areas where avalanches are most likely to occur. The regionalisation of both ERA5-Land and MeteoMont ds and DH3gg is performed by applying the index value regional method before the bias correction and the downscaling of ERA5-Land data as, in terms of computational efforts, only 2 bias corrections and downscalings for each couple of best-matched ERA5-Land and MeteoMont homogeneous areas would be required instead of 102 (2 for each couple of nodes and stations). The bias correction and downscaling of the ERA5-Land regionalised variables are then performed by means of a statistical transformation based on the assumption that said variables are described by one of the distributions belonging to the GEV family. This work is of particular relevance as, on the one hand, it overcomes the limited availability of snow information in the Central Apennines, especially in relation to avalanche related applications. In fact, it provides a tool that quantifies ds and DH3gg quantiles at elevations and sites that are not supplied with observations. On the other hand, it provides realistic initial and boundary conditions for simulating avalanche dynamics, drawing up hazard and risk maps, and designing active and/or passive defence structures.

In the era of climate change induced by global warming, it becomes fundamental to consider the long-term variation of physical parameters needed to define design loads or to perform risk assessment. In the scientific community, the IPCC provides an assessment report on climate change approaching a wide range of issues including the impact on the environment and potential mitigation and adaptation strategies, at a global level (Brasseur, 2022). In the coastal field, it is expected that climate change will influence wind patterns, sea levels, storm surge characteristics and their frequency. This will have an impact on wind-generated waves and on the variation of its synthetic parameters that will characterise coastal flooding phenomena in the near future, especially along low-lying coasts. In this context, climate change may induce modifications to wave intensity and direction so, this could have detrimental effects on coastal areas. Furthermore, it has been substantiated that the combination of rising sea levels, wave run-up and storm surge events will enhance the role of coastal flooding in the management of coastal areas and in the definition of long-term adaptation strategies (Pasquali et al., 2023; Pörtner et al., 2019). The quantitative estimation of impacts of climate change can be then identified as primary aspect to be dealt with the definition of adaptation strategies (von Schuckmann et al., 2023). The functionality of coastal and harbor infrastructures and the evolving threat of coastal flooding highlight the critical importance of investigating the potential impacts of climate change. Due to this, there is clearly a need for implementing enduring adaptation strategies, allowing to incorporate them into land-use policies and effective management practices (De Girolamo et al., 2017; Pasquali et al., 2023; van Gent, 2019).

Water hammer waves, i.e., low-frequency, low-Mach number propagation of finite-amplitude pressure waves in pipe flow, are investigated by means of the wave equation proposed in Di Nucci et al., 2024a, 2024b. The wave equation, resembling a linear damped wave equation, comes from the turbulent-viscosity model based on the quasi-incompressible Reynolds Averaged Navier-Stokes equations. Changes in temperature due to entropy production are neglected, and adiabatic conditions are imposed. Additional insights on the assumptions used to derive the wave equation are also provided. Focusing on the one-dimensional propagation of pressure waves in liquid-filled pipes (without cavitation), analytical solution of the wave equation is tested against experimental data available from the literature. The impact of the simplifying assumptions on the quantitative outcomes appears to be small; therefore a good level of accuracy in replicating water hammer wave characteristics (including damping, smoothing, and maximum pressure peak) is achieved. Results show that the Reynolds number has minimal influence on water hammer wave propagation, i.e., the vorticity field has no remarkable effect on flow behavior. Deeper attention is given to entropy production, and to the role played by the dimensionless number which is identified as predominant in water hammer wave propagation. Damping properties are also determined.

Cyclones represent a natural event characterized by a system of winds rotating inwards to an area of low barometric pressure, with an anticlockwise (northern hemisphere) or clockwise (southern hemisphere) circulation (Wang, 2012). Many operational warning systems rely on complex numerical hydrodynamic models to provide surge and flood forecasts (Pasquali et al., 2015). Numerical simulations are usually carried out by defining the pressure and wind field representing the given cyclone to force the numerical model. The large extension of the domains of interest and the complexity of the phenomenon make the numerical models characterized by high computational costs. A possible approach could be reducing the dimension of the numerical grid but in this case, the solution would be influenced by the boundary conditions. This research work aims to propose a novel analytical approach able to describe hurricane-induced storm surge (modeling both temporal and spatial variations) useful to define reliable boundary conditions to be used within hydrodynamic simulations with reduced domain dimensions, hence reducing the computational costs of detailed numerical simulations.

In the last years, BIM methodology has been particularly used in the buildings and civil infrastructures fields such as bridges, roads, and railways design and maintenance. The same cannot be said regarding maritime infrastructures, i.e. for design and maintenance of harbor and coastal structures. The Standard-definition provided by U.S. National BIM can be recalled to better understand BIM’s potentialities in maritime infrastructure design and maintenance: “BIM, Building Information Modeling is the digital representation of physical and functional characteristics of a facility creating a shared knowledge resource for information about it and forming a reliable basis for decisions during its lifecycle, from the earliest conception to demolition” (Deshpande et al., 2018). It is clear that the model is much more than a simple (geometrical) 3D model and that its usage can be extended to whatever the “facility”. Indeed, in a BIM model, different models can be implemented, from financial ones to geometry or graphical ones. In other words, every project generates a flow of information that is shared by the design teams and other stakeholders over the whole lifecycle of the facility.

Under adiabatic conditions, and neglecting temperature variations due to entropy production, we present a set of Reynolds Averaged Navier–Stokes (RANS) equations for fluids of low compressibility, i.e., fluids in the liquid state. In the low Mach number limit, we specialize the RANS equations to the one-dimensional unsteady pipe flow, and we deduce the dimensionless number that plays a predominant role in the flow behavior. We reduce the system of equations to a linear damped wave equation, and use its analytical solution to investigate the propagation of large amplitude pressure waves in liquid-filled pipes (water hammer phenomenon). We test the model reliability by comparing the analytical solution of the proposed model against experimental data available in the literature.

Historical maps, aerial photos, and satellite images are often used to investigate coastal area conditions and their historical evolution, in terms of shoreline location, coastal structures deployment, and anthropic pressure. The application of multi-temporal shoreline extraction by combining historical aerial photographs and tri-stereo Pleiades images of the littoral cell bounded by Capo d’Anzio and Circeo headlands (Central Italy, Lazio region, Tyrrhenian Sea) is illustrated and discussed in this paper. The analyzed coastal area presents great environmental and tourism values, mainly due to the presence of the Circeo National Park, and its Special Protection Areas (SPAs) and Sites of Community Interest (SCI), belonging to the Natura 2000 network. The area is also characterized by its own high morphological vulnerability due to the absence of sediment supplies and the presence of coastal structures in the updrift area that trap, at least partially, the incoming longshore sediment transport. The available aerial photographs and satellite images have been orthorectified by using aero-triangulation and rational function techniques, respectively. The digitized shorelines, spanning from 1954 to 2019, have been used to gain insight into the advancing/retreating coastal stretches along the area, by applying the Transect Based Analysis and the Area Based Analysis. The obtained results have been related to the Lazio region coastal management measures, implemented within the same time frame.

We frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz–Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier–Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier–Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.

The ongoing urbanization motivated past research works on pollutant transport in urban areas. Indeed, impermeabilization of the soil has detrimental impacts on evapotranspiration, filtration, and recharge of groundwater. Besides the waterproofing of urban surfaces, the presence of elements such as roads, parking lots, roofs, and sidewalks enhance the build-up of pollutants on the surfaces during dry weather periods while contributing to the increase in the runoff volume. The hydrological and hydraulic characterization of urban catchments allows for identifying the pollutants that influence the water quality, particularly in coastal areas. This aspect is crucial to identify the most appropriate measures to preserve the quality of water receptors and to ensure their specific uses. Sustainable urban drainage systems (related to the Low Impact Development approach, i.e. LID) have been identified as appropriate practices to address these issues. They aim to control stormwater and its quality through low-impact technologies, which exploit natural resources and are conceived to mimic the water regime in the pre-urbanization configuration. This work aims to evaluate the effects of LIDs within the frame of an in-depth parametric analysis applied to an ideal urbanized area. The analysis relies on using hydrologic and hydraulic modeling to assess the influence of LIDs on water quality. For a given configuration and extension of LIDs, the influences of (i) duration of dry weather periods, (ii) rainfall intensity, and (iii) land use are investigated.

One of the possible effects of climate change is the increase in sea level extremes. Therefore, the evaluation of possible scenarios of change, also considering the increase of the mean sea level, may be a crucial point in the evaluation of hazardous events and, consequently, in future coastal planning and adaptation strategies. This work aims at investigating, from a statistical point of view, possible variations in extreme storm surges using the two climate change scenarios provided by the Copernicus Climate Change Service for the period 2041–2100 (RCP 4.5 and 8.5) compared with the current situation 1979–2017 (ERA 5 database). The analysis is applied to the case study of the coastal stretch of the Abruzzo Region that lies on the Adriatic Sea, which is particularly prone to coastal flooding driven by storm surge events (i.e., sea level variation). Return levels of extreme storm surges have been evaluated for both current and future scenarios to have a general picture of the future variation in coastal flooding areas analyzing also the possible future response of coastal structures (i.e., harbors, breakwaters, groins, etc.) to these changes to highlight the needing of adaptation strategies.