*6.1. Hydrodynamic Modeling*

Within the detailed modeling phase, hydrodynamics plays a crucial role. The selection of the models type and the accuracy levels of the modeling scenarios should be representative of the project-specific features and of the spatial and temporal scales of the main physical processes driving the sediment transport phenomena. Then, the analysis has to be based on the environmental conditions of the intervention site: the complexity of the models implies the knowledge about forcing terms and the geometry of the site.

Basically, the hydrodynamic modeling is aimed at estimating the kinematic field (i.e., water levels and currents) responsible for the plume dispersion into the computational domain. The system of governing equations is rather complex and solved by numerical models with a high computational cost. This allows the study of very small spatial domains and for short-duration time windows. To overcome this limitation some simplifications are needed. These simplifications modify the governing equations (and therefore the processes that they are able to reproduce) to allow the analysis of larger areas and for longer time windows. In order to simplify the equations, it is important to identify the crucial key factors forcing the hydrodynamics. Just as an example, wave action plays a key role in the re-suspension and dispersion of sediments in relatively shallow water, while it can be intended as a secondary factor in deep water, where stratified phenomena must be taken into account instead. Indeed, waves and currents interact and influence each other (wave-current interaction). The presence of wave motion generates alterations in the hydrodynamic field that are almost negligible offshore, but may become significant in coastal areas. Even in transitional environments, usually characterized by shallow depths and mainly influenced by tidal oscillations, the action of wind waves produces hydrodynamic effects (and consequently transport phenomena due to interaction with the seabed) that are often not negligible. In turn, also the currents field can generate variations on the wave field (i.e., refraction). This phenomenon may become of grea<sup>t</sup> importance in areas such as transition environments characterized by the presence of river mouths or coastal areas characterized by the presence of intense local currents (e.g., rip currents, [42]).

Based on the selected driving forces, short wave propagation and long waves effects may be solved within either a coupled or uncoupled approach. Based on the importance of flow stratification, either two- (2DH), three- (3D), quasi-three-dimensional (Q3D) or multilayer models have to be considered. Table 2 synthesizes the applicability of the considered model types for a series of relevant cases within the frame of the mathematical modeling of physical effects induced by marine sediments handling works.

When wave propagation is addressed as a main driving force, the coupled approach aims at describing wave propagation by obtaining a detailed description of its time and spatial propagation. On the other hand, the coupling may be carried out by using the numerical results obtained by a wave propagation model as the forcing term of a hydrodynamic model able to give currents and water levels on a time scale longer than the short-waves period (and vice versa when the effects of currents on the wave propagation have to be considered).

3D numerical models are based on the resolutions of approximated equations solved in the three-dimensional space. The approximations (e.g., Reynolds Averaged Navier Stokes (RANS), large eddy simulation (LES)) are needed to make the numerical models usable within the frame of reasonably large domains. Nevertheless, they are characterized by large computational costs and then they are appropriate only when extremely detailed studies are needed. Examples of these models are NEMO (e.g., [43]), MOHID (e.g., [44]), ADCIRC (e.g., [45]), MIKE3 (e.g., [46]).

On the other hand, 2DH, quasi-3D (Q3D), and multi-layer models are based on equations integrated along the vertical direction. The use of 2DH models is appropriate when dealing with marine-coastal environments in which the vertical dimension of the domain, i.e., the water depth, is significantly smaller than the horizontal dimension (e.g., coastal and transition areas). However, it is

necessary to pay attention to the applications for which the effects of vertical processes are important, such as stratified flows (e.g., river mouths with fresh water inlet in a salty environment) or wind driven circulation that can be characterized by high variations of the current profiles along the vertical direction. In such cases, it is possible to use models that, although not strictly three-dimensional, maintain information on the vertical variability of the quantities of interest (e.g., [47]). One approach is to hypothesize a given structure of the variability of quantities along the depth (Q3D models). Alternatively, it is possible to use several layers to integrate the governing equations by taking into account the flow stratification (multi-layer models). Examples of such a kind of models are SHORECIRC (e.g., [48]), DELFT3D-FLOW (e.g., [49]), MIKE21 (e.g., [50]), SHYFEM (e.g., [51]), POM (e.g., [52]), ROMS (e.g., [53]), SWASH (e.g., [54]), XBeach (e.g., [55]).

**Table 2.** Applicability of model type for a series of relevant cases, when model type as well as computational costs are accounted for. (++) suitable (even considering computational load with respect to expected results); (+): possible; (o): not completely suitable, hence the results may be affected by the model formulation; (-): not suitable, hence the results are strongly affected by the model formulation.


It has to be underlined that the hydrodynamic studies, i.e., the estimate of water levels and currents, need to take into account several driving forces in the computational domain and at the boundaries. The former, with different relevance depending on the area of application of the analysis (coastal and transitional areas, semi-closed basins, offshore areas), is made up of: wind and wave action, tidal oscillations, inlets characterized by different densities (e.g., river mouths or industrial discharges) for which it is necessary to take into account the buoyancy effects. The latter, on the other hand, consists of large-scale forcing, such as tidal induced currents and basin oscillations (e.g., wind setup, seiches).

The model must also take into account the physical processes related to the interaction of hydrodynamics with the boundaries of the area of interest (e.g., the sea bottom, the coastline and the open boundaries) as well as any elements placed within the calculation domain (e.g., coastal defenses, intertidal morphological structures in lagoon environments, bars or shafts in mouth areas, offshore structures if detectable by the resolution used in the model).
