The operational activities of harbors and ports are closely related to the local bathymetry, which must be sufficiently deep to guarantee the regular passage, maneuvering, and berthing of ships. However, ship clearance is often so limited that it threatens the safety of in-port navigation, and ships may even hit the seabed in extreme cases. Therefore, this is a critically important issue that often results in management and maintenance efficiency problems in terms of the bottom and a port's infrastructure in general (Mujal-Colilles et al., 2016; Castells-Sanabra et al., 2020).

The action of a ship's main propellers means that traffic in ports is responsible for generating intense current jets, as noted in Fig. 1. The high velocities induce shear stresses on the sea bottom, which can possibly result in sediment resuspension when they exceed the critical stress point for erosion (Van Rijn, 2007; Soulsby et al., 1993; Grant and Madsen, 1979). Before depositing back onto the seafloor the resuspended sediment may be transported widely around the basin by the combined effects of natural currents, such as those induced by tides, winds, or density gradients, and by vessel-related currents, such as those induced by the propellers or the movement and displacement of ships. Thus, the continuous traffic in and out of ports can result in the displacement of a huge volume of seabed material, which can then induce significant variations in the bathymetry over medium to long timescales. The formation of erosional or depositional trends in specific areas of port basins can potentially result from these variations.

If such dynamics are particularly pronounced and rapid (bottom accretion of the order of tens of centimeters per year or even higher), the port authorities must carry out dredging operations for the maintenance of the seabed, in order to fully recover the clearance and ensure the conditions necessary for undisturbed ship motion, maneuvering, and docking or undocking operations.

Most of the published literature about the effects of ships' propellers on port sediments and structures is experimental, and it has mainly been conducted in laboratories using physical models (Mujal-Colilles et al., 2018; Yuksel et al., 2019). Few practical instruments are available for port authorities that can provide robust and scientifically based analyses and predictions of the relevant processes. Such tools can enable managers to plan specific actions aimed at maintaining the seabed, thereby helping to guarantee the continuity of operational activities of ports and to optimize the use of economic resources. Unplanned maintenance activities usually involve additional costs due to the need to operate under emergency conditions and, in some cases, partially interrupt the service.

The integrated numerical modeling of hydrodynamics and sediment transport represents an important aid to port authorities and, more broadly, to port managers and operators, as suggested by Mujal-Colilles et al. (2018). This can reproduce and thus provide a better understanding of the seabed sediment dynamics induced by ships' propellers over short, medium, and long timescales, thereby establishing what tools are required to ensure the efficient operational maintenance of the seabed.

Propeller-induced jets have mainly been studied using empirical formulas based on specific characteristics of the ships and ports of interest, such as the bathymetry; propeller typology, diameter, and rotation rate; and the ship's draft. The most common approaches are the German method (MarCorm WG, 2015; Grabe, et al., 2015; Abromeit et al., 2010) and the Dutch method (CIRIA, 2007). The resulting induced velocities are usually only considered locally to inform the technical design of mooring structures and the protection of a port's infrastructure. Although various assumptions are introduced through empirical formulas, these approaches are limited and do not fully consider the three-dimensional evolution of the induced jet throughout the water column at any distance from the propeller or at any location of the port. Therefore, these tools are not suitable for the comprehensive management of ports.

We conduct a pilot study of the hydrodynamics and seabed evolution induced by ships' propellers in the passenger area of the port of Genoa (Fig. 2), where the marine traffic involves mainly passenger vessels (ferries and cruise ships, generally self-propelled) and in which the resulting sediment dynamics in terms of erosion and deposition rates are particularly significant: estimated to be of the order of several tens of centimeters per year (as directly estimated and communicated by the port operators and via an analysis of bathymetric surveys). In this study, we propose that the integrated high-resolution numerical modeling of three-dimensional hydrodynamics and sediment transport can be a robust and science-based tool for the optimization and efficient planning of port management and maintenance activities. We propose a new methodology that can be used in a delayed mode and can, thus, reproduce the historical major sediment processes over time, as in this study, or in a prediction mode through the potential implementation of real-time operational services.

The remainder of this paper is organized as follows: in Sect. 2, we introduce our methodology; the data available for the study are presented in Sect. 3; Sect. 4 describes the numerical models used; the results of the numerical simulations are presented and discussed in Sect. 5; and the summary and conclusions of the work are given in Sect. 6.

The study is based on the latest versions of the hydrodynamic and mud transport models MIKE 3 FM (DHI, 2017), which are described in detail in Sect. 3 and in Appendices A and B. A very high resolution was used in the numerical model to realistically reproduce the propeller-induced jet, both in the vertical and in the horizontal, at approximately 1–2 and 5 m, respectively. Together with a non-hydrostatic version of the hydrodynamic model, this enables the processes and dominant patterns of the current field generated by the ships propellers during the navigation and maneuvering inside the port to be reproduced very accurately.

As shown in Fig. 2, 12 docks have been included in the study (marked with orange or red lines indicating ferry or cruise vessels, respectively). The port authority mainly focused on passenger vessels, as they considered their effect on the seabed to be greater than other types of vessels that have much less frequent passage. Moreover, passenger ships generally self-propelled, whereas other vessel types are often driven by tugboats. Therefore, we only simulated passenger ships.

The turning basins in which arriving vessels undergo maneuvers for berthing are represented by the white dashed circles marked “a” and “b” in Fig. 2. Circle a refers to vessels berthing at docks T5 to T11, whereas circle b refers to vessels berthing at docks T1 to T3. Finally, the turning area for vessels arriving at docks D.L., 1012, and 1003 is at the entrance of the port and is not simulated in this study, as it is outside of our area of interest.

The general methodology can be separated into the following four phases:

Assessment of the marine traffic during a typical year. This phase is fundamental, as it identifies the typical dynamics of the marine traffic in the different sectors of the port and the characteristics of the ships that have the greatest effect on the hydrodynamics and sediment resuspension on the bottom. These include the size of the ships, the related draft, the dimension of the propellers, and their typical rotation rates. The results of the analysis, which are discussed in detail in Sect. 4.1, also enabled representative synthetic vessels for each berth of the port to be defined.

The proposed approach assumes that each hydrodynamic and sediment transport simulation uses the same bathymetry as the initial bottom condition. Although this assumption may have implications, as we explain in the results section, it does not compromise the main conclusions of the study.

Most of the data necessary for this project were provided by the Port Authority of Genoa and Stazioni Marittime SpA, the main port operator in the area.

The non-hydrostatic version of the MIKE 3 HD flow model (DHI, 2017) was used to simulate the propeller-induced three-dimensional current along the port basin. The resulting hydrodynamic field was coupled with the sediment transport module MIKE 3 MT (DHI, 2019), which is suitable for fine-grained and cohesive material, in order to drive the erosion, advection and dispersion, and deposition of fine sediment along the water column.

The main results of the hydrodynamic and sediment transport model are presented in this section. Due to the large number of simulations carried out, only those regarding two docks are shown. However, the current and sediment concentration results corresponding to the other simulations are qualitatively similar. We focus on the simulations of docks 1012 and T7. dock 1012 is particularly important as it hosts the largest passenger vessels operating in the port, whereas dock T7 has a high frequency of passages.

Figure 7a and b show the propeller-generated current in the bottom layer and at the depth of the propeller's axis, respectively, and Fig. 7c and d show the corresponding resulting suspended sediment concentration in the same layers during the departure of a cruise vessel from dock 1012. The characteristics of a vessel representative of the traffic in the dock are given in Table 1. When departing, the engine operates close to full power, which we assume results at a rotation rate of 2 rps for the propeller. This induces a maximum velocity at the depth of the propeller axis close to 9 m s-1, which is damped to approximately 2 m s-1 on the bottom of the berthing basin along the vessel's route. This intense jet is deflected to the left due to the head wall of the berthing basin, which constrains the flow and induces a cyclonic eddy that is well-developed along the whole water column. The cone-like envelope of the jet in the vertical plane, as illustrated in the theoretical scheme of Fig. 1, can be observed in Fig. 7a and b, which refer to the same example: the influence of the propeller on the bottom occurs several tens of meters behind the propeller's position, and the velocity at the bottom is much reduced. The induced eddy in the wet basin acts as a trap for the eroded sediment, which enters the cyclonic gyre (or anticyclonic gyre in the case of departure from the opposite dock) and tends to deposit in the middle of the basin, where the fluxes progressively decrease. The position of the eye of the cyclone evolves parallel to the docks' longitudinal walls and induces the sediment trapped inside the gyre to sink along the longitudinal axis of the wet basin. Such dynamics occur similarly for all the horseshoe-shaped wet basins, inducing accumulation along the central portions. The resuspended sediment may reach very high concentrations of up to several hundreds of milligrams per liter in the bottom layers, depending on the different specific characteristics of the sediment texture (such as grain size, level of consolidation, and availability to erosion) and of the vessel (such as dimensions of the propellers, rotation rate, and draft).

Various hydro and sediment dynamics occur during the inbound phase of vessels maneuvering inside the port. Most of the maneuvering operations (i.e., when vessels rotate within a turning basin and proceed backwards to the docks) occur in the turning basins denoted by the dashed circles a and b in Fig. 2. The engines operate at high power when starting the maneuver to allow for the rotation of the ship. The vessel's longitudinal axis then rapidly changes direction (from tens of seconds up to a few minutes) and can span wide angles, depending on the specific maneuver. The propeller-induced jet follows the same rotation along the horizontal plane, resulting in a fan-like distribution of directions for the associated currents. Such operations are realistically represented by the model, as shown in Fig. 8, which refers to the berthing of the vessel representative of dock T7. The currents shown in the figure are those associated with the propeller's axis during four different moments of the turning maneuver. Each panel refers to successive time intervals of approximately 100 s. These successive instants are presented in the following order: upper-left panel, upper-right panel, lower-left panel, and lower-right panel. In the lower-right panel, the propeller has already changed rotation direction and the vessel is now proceeding backwards. Thus, the induced current jet is heading towards the center of the port and pushing the sediment towards this area. The simultaneous seabed activity is shown in Fig. 9. Although the jet-induced currents are much weaker at the seabed than those at the depth of the propeller's axis, they are still significant and may reach intensities of up to 1 m s-1, depending on the local bathymetry.

The current distribution at the seabed is much more chaotic than at the propeller's axis depth. This area of the port corresponds to the natural pit (which reaches approximately 22 m below the surface in the deeper part) in which the material dredged from the accumulation areas is often dumped during the sea bottom maintenance activities. The dashed line shown in the lower-right panels of Fig. 8 and Fig. 9 refers to the transect presented in Fig. 10, for the same instant (i.e., when the vessel has ended the maneuver in circle b and is approaching dock T7 backwards).

A combined analysis of Figs. 8, 9, and 10 helps us understand the dynamics occurring in turning basin b during the maneuvers when approaching docks T5, T6, and T7, and particularly the overall sediment dynamics of the entire port, as these three docks account for approximately half of the entire passenger traffic. The propeller-induced velocities at the bottom of the natural pit during turning maneuvers are variable and may exceed 1 m s-1, which is a significant current intensity that can entrain and move a large amount of sediment. The resulting resuspended sediment concentration may reach values exceeding 50–60 mg L-1, as shown in Fig. 10b. Once resuspended from the pit, the sediment is advected by the jet-induced complex field of currents of Figs. 8 and 9. This area is typically refilled with freshly dredged material resulting from the seabed maintenance activities; thus, the propeller-induced currents on the bottom have an enhanced erosion effect on the unconsolidated material and can rapidly nullify the benefit of the dredging operations. Hence, the results of the simulations suggest avoiding the use of the natural pit as a dumping area for the resulting material, and they confirm that integrated modeling can be an effective tool for simulating the processes and mechanisms related to sediment transport as well as for the optimized planning of maintenance activities.

The impact of the marine traffic on the bed thickness is illustrated in Fig. 11, which presents the erosion and deposition maps resulting from the simulations of one departure (left column) and one arrival (right column) of the representative passenger vessels of docks 1012 (top row) and T7 (bottom row). Blue represents areas of erosion, and red represents the accumulation of the sediment after an interval of time long enough for the resuspended sediment to completely settle. The left column Fig. 11 shows that a considerable amount of material tends to be eroded from the bases of the docks during the vessel's departure and then settles in the center of the mooring basins. This mechanism is clearly related to the vessel's departure (left column) rather than its arrival (right column). The erosion underneath the vessel's keel along its trajectory is evident, both during departure and arrival, thereby supporting previous experimental findings (Catells et al., 2018). The magnitude of the erosion and deposition of a single vessel's passage is of the order of a few millimeters in the areas most influenced by the vessel's activity.

Such an impact can become a real threat to the continuity of operations in large and busy ports such as Genoa over medium to long timescales. The few millimeters of accumulation and erosion can become several tens of centimeters after a few thousand annual passages. For the sake of completeness, the results of the impact on the bed thickness due to the activity of the other vessels not shown in the main body of the text are presented in Appendix C.

Based on the traffic analysis in Table 1, we projected each single marine passage to a 1-year duration and superimposed the effects of erosion and deposition of vessels that are representative of all of the passenger docks. Thus, we were able to reconstruct the annual port seabed evolution for the year of 2017. The effects of the single passages were weighted by the specific occurrences of that year, which resulted in 24 maps (one for each docking and one for each undocking), and the results were integrated to obtain a final map.

As the trajectories for reaching a dock (or departing from it) vary slightly from passage to passage, a Bartlett spatial filter was applied to the integrated results using the values of 4, 2, and 1 as weights. Figure 12 presents the results of this analysis. In the left panel, the results from the modeling system in terms of annual erosion (blue) and accumulation (red) are shown, and in the right panel, the observed seabed evolution is shown. The observed map was reconstructed using the outcomes of two bathymetric surveys carried out in the May–June 2017 and March–June 2018 periods. The difference in the bathymetries of the two surveys resulted in the evolution of the seabed during the approximate 1-year period, except for dredging operations. We indicated the areas where the most significant dynamics took place on the maps using numbers.

The area between the heads of Ponte dei Mille and of Molo Vecchio, identified as 1 in Fig. 12, was dredged during the October–December period in 2017, and approximately 15 000 m3 of solid material was removed and dumped into the natural pit of the port, as indicated by the number 5. Thus, what, at first sight, appears to be an area of erosion due to vessel traffic – area 1 in the right panel of Fig. 12 – is actually an area of accumulation, which is confirmed by the fact that dredging operations were conducted. Similarly, the accumulation observed in area 5 (right panel of Fig. 12) is not the result of the induced action of the propellers but of the accumulation of the sediment dumped after the maintenance dredging operations. The model results are in total agreement with these dynamics. As discussed above, the material resuspended during vessels' maneuvers is likely pushed towards area 1 in the phase during which the vessels approach the docks backward. Conversely, area 5 is partially an area of erosion, as evidenced by the model. The freshly deposited material during dredging operations is thus rapidly resuspended.

Area 1 accounts for approximately 30–40 cmyr-1 of accumulated material, with local maxima of up to 50 cmyr-1. Similar values were estimated through years of managing experience by the personnel of Stazioni Marittime S.p.A (Edoardo Calcagno, personal communication, 2019).

The central portions of the wet basins marked with number 2 in Fig. 12 are areas of deposition, mainly due to the departure phase of the ships. Again, the model can efficiently reproduce both the accumulation along the central parts of the basins, where it may reach 20 cmyr-1 or even more, and the erosion along the walls of the docks. Here, the propellers' erosive action may result in stability problems for the docks, particularly along the walls of dock 1012, where the biggest cruise vessels operate.

The erosion underneath the vessels' typical routes (i.e., from the entrance to approximately the center of the port) is also well represented by the model (identified using the number 6 in Fig. 12). The model and the observations also exhibit good agreement in the deposition area (number 7), where a local gyre forms and entraps the suspended sediment. Finally, areas 3 and 4 are also subject to deposition, and qualitative agreement between the model and the various bathymetric surveys is evident from Fig. 12. The erosive print observed in the survey under these areas is most likely due to activities related to cargo vessels approaching and departing from dock Calata Sanità. These vessels were not the focus of our study, and Calata Sanità only operates container ships; thus, the model does not include the marine traffic in this area.

In general, the observed and the modeled annual evolution of the port seabed show very good agreement, which confirms the reliability and robustness of the hydrodynamic and sediment transport model and demonstrates the potential importance of an integrated modeling approach in optimizing the management of port activities.

The assumption of unvarying initial bathymetry conditions in the different scenarios deserves some additional consideration, as it undoubtedly introduces some inaccuracy into the results. This approach does not consider the real order of vessels' passages or the impact that the evolving seabed has on the hydrodynamics and sediment transport simulations. In particular, the variable clearance distance between the propeller's tip and the seabed due to the evolving erosion and deposition processes is not considered, although this will increase the differences over time. However, the complexity of the system requires the introduction of several approximations, such as the dimension and rotation rates of the propellers, the typology and distribution of the sediment, the layering of the sea bed, the shear stress for erosion and deposition, or the constant initial bathymetry. A solution for the bathymetry issue could be to implement the system in operational mode and, thus, continually update the initial bottom boundary conditions through the simulation iterations. However, this was not realistic in terms of computational effort and was beyond the scope of the study, which was to identify areas of erosion and deposition in the port and to evaluate the order of magnitude of the corresponding evolution rates to support the port management. Nevertheless, if we consider the most significant variation in the seabed and the typical propeller-induced bottom velocities, which are of the order of 50 cm (Fig. 12) and 1–2 m s-1 (Figs. 7, 9, and 10), respectively, the resulting bottom shear stresses are of the order of 2–4 N m-2. Such values are orders of magnitude larger than the typical critical shear stress for the deposition and erosion of freshly deposited fine sediments (of the order of 0.07–0.15 N m-2, respectively), suggesting that variations in the bottom shear stresses due to a change in the clearance distance of the propeller's tip of the order of 50 cm (a conservative estimate) would not have a significant impact on the mobility of the sediments. Consequently, such differences would not imply substantial variations in the erosional and depositional processes and patterns.

The impact of marine traffic on the seabed of the passenger port of Genoa was investigated through numerical modeling. The combination of a very high-resolution, non-hydrostatic, circulation model (MIKE 3 HD FM) with a sediment transport model (MIKE 3 MT FM), based on unstructured grids on the horizontal and on sigma levels on the vertical, enabled us to reconstruct the annual evolution of the port seabed. The final results of the modeling, in terms of maps of erosion and deposition inside the basin, were qualitatively supported by observational evidence. Our approach was to simulate only one arrival and one departure from each dock of the port and to analyze the impact of a single marine passage on the seabed in terms of sediment concentration, motion, and distribution.

From the traffic analysis in the port for a typical year (2017), we could obtain the detailed situation of the number of arrivals and departures for each dock as a starting point for the study. By superimposing the effects of single vessels weighted for the annual number of passages of the most representative vessel operating on each dock, an annual map of erosion and deposition was reconstructed and validated on a semiquantitative basis by comparison with various bathymetric surveys for the same period.

In general, the simulations showed that the velocity intensities on the bottom induced by propeller-generated jets can reach almost 2 m s-1, and mainly depend on the dimensions of the propellers, the rotation rate, and the distance between the propeller and the bottom. Such velocities may reach up to 8–9 m s-1 at the propeller's axis depth and penetrate horizontally through the water for long distances, up to at least 40–50 times the propeller's diameter. The bed shear stresses induced by these velocities as well as the propeller jet-induced entrainment, mobilize and resuspend large amounts of the fine and less compacted sediments present inside the port. Fine proportions with lower fall velocities tend to remain in suspension for longer periods of time, resulting in the creation of sediment plumes.

Our findings showed how significant these deposition rates can be in a densely operated port, reaching values of several tens of centimeters per year in specific areas.

Our approach enabled us to minimize the computational time and also decompose the overall complex view of sediment transport of the entire port into several simpler views. Consequently, we were able to analyze the specific hydro and sediment dynamics for each dock and vessel, and to identify specific routes responsible for particularly serious erosion and accumulation, as historically reported by the management authorities of the port operations and traffic. The range of current intensities induced by the propeller action was identified along the water column, and this can be further used as a sound and scientifically based benchmark value for potential defensive actions on the seabed and port structures in order to guarantee the ongoing full operability of the port.

The most significant mechanisms for the port's hydro and sediment dynamics that occur during vessel passages were identified and the subsequent analysis identified how and why specific areas are subject to erosion and other areas are subject to deposition as well as the extent of these mechanisms. In particular, the mechanism of ongoing erosion along the docks' walls and of deposition along the central portions of the mooring basins were identified and explained, along with the ongoing deposition process in the area between the heads of Ponte dei Mille and Molo Vecchio. Identifying and reproducing this process for the port managers was particularly important, as it occurs at a very significant rate of up to 40–50 cmyr-1 in some areas. Finally, the natural hole located off the heads of Ponte Colombo and Ponte Assereto was identified through the model as an area of erosion, although at significant depth. This is mainly due to the turning maneuvers carried out by vessels in this area, and the area partially corresponds to one of the turning basins of the port and involves approximately 50 % of its entire traffic (docks T5, T6, and T7). This location has historically been used as a dumping site for the material resulting from seabed maintenance dredging, but our study showed how unfit this area is for such a purpose, as the freshly deposited sediment is soon resuspended by the intense currents induced by the vessels' turning operations.

The importance of this study is not only to confirm how integrated high-resolution modeling can reproduce the most significant and complex mechanisms of hydrodynamics and sediment transport occurring inside ports, which was successfully achieved, but it also suggests that it can be used as a tool for optimizing port management. It could be applied to regulate the marine traffic in ports and, thus, identify the most suitable schedule and routing in terms of sediment concentrations, bottom velocities, erosion, accumulation, and vessel drafts. It could also be used to identify the largest vessels that can potentially operate in the docks when planning future commercial traffic or to study the impact of increased port traffic on the seabed and on the port's structures. Finally, in recurring dredging operations, most busy ports must regularly face sediment accumulation problems, and our tool can inform awareness planning of such activities so that authorities are fully prepared.

Daily fully operational implementations of similar integrated systems can also be set up, as the daily schedule of the port is known. This would enable the continuous monitoring of the evolution of the seabed and allow authorities to be constantly and fully aware of the potential critical issues that they face.

Future research following on from this study should also consider the effect of the Bernoulli wake in combination with the propeller-induced jets on sediment resuspension, advection, and dispersion. This mechanism was not considered in the present version of the system. The current intensities caused by vessel-generated waves during and after their passages will be smaller than those induced by propellers along their axes, but they tend to penetrate along the water column and reach the bottom, thereby carrying a significant amount of energy and possibly resuspending a substantial amount of solid material (Rapaglia et al., 2011), which is likely to enhance vertical mixing and may induce the sediment to be suspended for longer periods and at higher depths.