A literature search was carried out for peer-reviewed publications between the years 2020 and 2025. Databases such as Scopus, Web of Science, and Google Scholar were searched using keywords such as “propeller-induced scour”, “CFD scour modeling”, “jet erosion”, or “coastal infrastructure scour”. While searching for publications, the titles and abstracts were filtered to select publications that were relevant to either the hydrodynamics of propeller jets or the scouring of sediments or related studies of numerical models for engineering purposes. A total of 37 publications were selected for this literature review.

The erosive force of the propeller depends on the characteristics of the turbulent jet it generates. One of the experimental correlations for such jets is that the maximum velocity of efflux (U₀) is always found at about 0.5 times the diameters of the propeller downstream of the plane of the propeller [8]. The velocity distribution in such a jet decreases axially with a rate of decay that is one of the major factors responsible for the bed shear stress. It is found that the velocity distribution is affected by the hub of the propeller, resulting in a bi-velocity peak, and that the swirling velocity does not affect it significantly [8][9].

This is important information for simplifying models representing real-world complex phenomena but could potentially neglect some complex interactions, such as that of maneuvering, where some influences of swirl velocity could appear in sediment entrainment.

One of the key considerations is the presence of boundaries. As a jet approaches the seabed or the quay wall, it is drawn to the boundary by the Coandă effect, with the attendant reduction in lateral dispersion and enhanced boundary flow speeds [9][10]. Huang et al. [11] showed that in recessed areas with small clearance heights (Z_b/D_p < 1), the boundary jet-attachment process can extend the area of high seabed shear stress. A major limitation of current hydrodynamic models is their focus on steady-state or “bollard-pull” conditions. Almost all of the foundational works, including the more popular literature reviews, investigate fixed propeller configurations, disregarding the dynamic influences of a moving body, in which the coupling between the jet phenomenon and a time-varying inflow field could appreciably influence jet growth as well as bed impingement [8][11].

The presence of a solid boundary significantly alters the scouring effect. When an unconfined jet hits a flat seabed, a scour hole is formed with geometry dependent mostly on the energy of the jet as well as the bed material properties [12]. A jet striking a vertical quay wall, on the other hand, becomes confined, resulting in the development of complex three-dimensional vortex systems (such as wall or horseshoe vortices) that enhance erosion [5][13]. This amplification of scour depth by the presence of a wall was measured to be 50% - 70% by Cihan et al. [5], whereas the merging of scour holes with unique geometry was observed by Cui et al. [12] for twin-propellers striking a wall.

It is observed that the rotation of the propellers (whether it is external or internal in twin systems) affects the point of maximum scour depth in the cross-direction by causing differences in the merging of twin jets [6][13]. Nonetheless, the current study offers a simplification by identifying “confined” or “unconfined” conditions. But in real-world harbor operations, the jet could quickly change between the two conditions or remain partially confined by sloping banks or rubble mounds, which is not captured adequately in existing literature.

Scaling from the results of models to prototype predictions is an engineering tradition, accomplished by means of densimetric Froude similitude [6][10]. This allows the ratio of inertio- to gravitational forces on sediment particles to be scaled consistently and has been shown to work for the prediction of scour depth at equilibrium. More recent theoretical efforts, however, aimed at finding more basic models of scaling. Scaling models for equilibrium scour of sediments by a turbulent wall jet were developed by Dey & Ali [13] or Lu et al. [14] by means of dimensional analysis and turbulence models. These models propose a “wall jet scour number”, which expresses jet velocity, scale, grain size, and critical shear velocity. This idea offers a very attractive theoretical basis, which goes clearly beyond empirical models [14][15].

A critical assessment of such work indicates that there is a certain contrast between theoretical models and their ability to work in practice. Although these new scaling models work very well with regard to the historical data sets employed, it is important to note that such validation is practically limited to classical wall jet tests and, by no means, to rotating propeller jets with their characteristic rotation and turbulence. Moreover, as it is observed by Wei et al. [9], some issues with regard to the turbulence intensity or transport modes (bedload or suspension) remain to be resolved for Froude models, avoiding possible anomalies in calculating rates of scour development.

On a positive note, it is certain that the engineering community would appreciate some efforts to validate new theoretical models of propeller scour on a large scale.

There is a widely documented three-stage pattern of propeller scour development: initial rapid growth, a phase of reduced rates of the process, and finally, an equilibrium phase [10][16]. Initially, the rates of scour development are very vigorous; it is documented that more than 60% of the total scour depth can develop in the first tenth of the total development time [10][17]. These vigorous rates of development pose critical challenges to the monitoring of infrastructure development stages before an obvious equilibrium is reached.

Equilibrium timescales are extremely uncertain. In laboratory flume experiments, for example, equilibrium can be reached in a matter of hours [17], whereas in the real situation, intermittent scouring timescales could be of the order of years [1][18]. This difference is one of the significant drawbacks of laboratory experiments, since here the propellers work continuously, whereas the real situation involves aggregate periods of high thrust in brief instances of berthing or maneuvering. Additionally, it is also found that in the real situation, lower levels of equilibrium are usually observed, as opposed to laboratory experiments [1][2]. This is likely due to the presence of natural variability in sediments, armoring, or periodic replenishments through natural transport of sediments into the area—a situation that is not taken into account in laboratory experiments. An interesting laboratory observation of “jet flipping” in wall jet experiments, where the jet switching between bed-attachment and surface-attachment modes results in periodic scouring and fill, implies that the situation of equilibrium is not fixed in many real-world flow situations [19].

Although helpful as a theoretical construct, there is considerable variability in real-world timescales for development with flow intensity (F₀), type of sediments, and boundary conditions. Real-world timescales for scour at the field scale could potentially be longer on account of scale effects and seabed properties [9][11]. “Equilibrium” in real-world applications is more likely a state of dynamic equilibrium, where scour is effectively negligible over engineering timescales (Figure 2).

Figure 2. Temporal development of propeller-induced scour depth, showing the characteristic three-stage evolution: rapid initial scour (Stage 1: 0 - 2 hours), slower development (Stage 2: 2 - 8 hours), and approach to quasi-equilibrium (Stage 3: 8+ hours). Model curve corresponds to logarithmic growth for clear-water scour. Experimental data points indicate variability of laboratory results [9][11][20].

Systematic experiments have revealed the major factors that contribute to the extent of scour. Bed shear stress, calculated from jet velocity just above the bed, is the principal erosive agent. It is most sensitive to the clearance height of the propeller (Z_b), with various experiments clearly indicating an inverse relationship, where shorter clearance height caused maximum scour depth with a resulting change in the hole geometry [5][10][20]. The densimetric Froude number (F₀, defined as the ratio of jet velocity to the submerged settling velocity of sediment particles, reflecting the relative importance of inertial to gravitational forces) is found to significantly indicate the scour depth, being a major input for various prediction relations for scour depth [5][6][20].

However, the relationship between these variables is complicated and nonlinear. For example, the role of the wall clearance (X_w) with respect to scour depth is important only up to a certain point (approximately 8D_p) beyond which it ceases to be effective [20]. Again, the impingement angle of the jet determines the geometry of the scour, with higher impingement angles resulting in narrower scarps [16]. The engineering issue here is that these variables are interrelated. A change in the draft of the vessel (which affects Z_b) with respect to cargo operations will mean that there is a corresponding change in the impingement angle as well. Currently, most of the engineering equations are of the form that each of these variables is independent, which could be a reason for the considerable scatter of data that is observed.

This depends largely on the type of sediments on the seabed. While for uniform sands that are non-cohesive, scour depth is inversely related to grain sizes, as more shear force is needed for larger grains to break away [15][21]. More research work is limited to this type of sand, understandably for obvious reasons, establishing a robust but limited body of knowledge.

Figure 3 shows the effect of the presence of clays on scour depth. Çihan et al. [5] gave a great contribution to the understanding of the effect of sand-clay mixtures by determining that a 5% - 10% mixture of clays significantly decreases the scour depth for low- to moderate-energy jets. Notably, for high-energy jets (F₀ > 11), the scour depth for clays was almost the same as that for non-cohesive sands, despite the electrochemical bonds between particles, revealing that there is a threshold energy beyond which hydrodynamic forces become dominant over electrochemical bonds. This result is of great importance for ports with muddy sediments but is limited to a study employing kaolin clays. A huge research gap is left for other clay materials.

Figure 3.Normalized scour depth (ε/D_p) as a function of densimetric Froude number for different sediment types. Non-cohesive sand has the maximum scouring ability. The critical value of 5% - 10% of clay mentioned by Cihan et al. [5] is transitional: 5% clays classify as sands for F₀ values larger than 11.3 since there is less scouring for lower F₀ values, indicating that it is a cohesive material. A threshold F₀ value of about 9 is observed for a purely cohesive material like clay for which there is little erosion below it [16].

Table 1. Summary of key findings from reviewed literature on seabed scour mechanisms induced by propeller jets.

In addition, natural seabeds are often graded or layered. This is observed by Duan et al. [4], who point out that “armoring layers” can form on these types of seabeds, with the finer material being stripped away, leaving a layer of coarse material that shields the seabed from erosion. This self-limiting effect is probably one of the major contributing factors for the difference between laboratory-predicted scour depths and real-world observations, and is never accounted for in current models of scour. Perhaps the biggest flaw in the current state of scour research is that it is almost entirely limited to uniform, non-cohesive sand.

Computational Fluid Dynamics (CFD) is the architectural foundation of current scour models. Reynolds Averaged Navier-Stokes (RANS) equations, solved with turbulence models k-epsilon or k-ω, remain the most widely used models of turbulence that strike the best ratio between solution accuracy and computational efficiency for engineering purposes [1]-[3][24]. For example, turbulence models of RANS type were successfully used for resolution of the horseshoe vortex system and the universal scour development around fixed structures, such as monopiles [2]. On the other hand, applying time-averaging to solve RANS relations could be inappropriate for resolution of important energy-containing fabric of turbulence, characteristic of strongly unsteady flows, such as those induced by rotating propellers [25]. In such cases, more accurate LES/DES approaches could be utilized for simulations [2][4] aimed at more profound research. Though these models provide significantly better predictability of mixing in turbulence and vortex phenomena, their great computational cost limited their application until now for such complex tasks as engineering-scale scour simulations [25][26].

Consequently, a pragmatic selection strategy emerges: RANS models are well-suited for large-scale engineering screening, preliminary design, or situations where computational efficiency is paramount. In contrast, LES or DES methods are restricted to forensic studies, basic research on turbulent physics, or situations where modeling the complex transient behavior of a propeller jet plays a crucial role in the problem under investigation.

One of the key challenges in the numerical modeling of scour caused by a propeller is representing the propeller in the CFD model correctly. This varies from a considerable simplification to a detailed representation. One of the ways of simplification is using the actuator disk or momentum source term, where essentially the effect of the propeller is simulated by adding momentum to the computational domains without necessarily requiring a detailed representation of the geometry [16][27]. This is a considerable simplification that helps reduce the computational complexity of the simulation, allowing for larger domains to be modeled with a considerable emphasis on far-field dispersion of the sediment cloud. Nonetheless, it is ineffective for modeling the complex turbulence, tip vortices, and boundary regional rotational flows that are important for bed scouring around the bed [27]. A more detailed representation is gained using the Sliding Mesh or Overset Mesh models, that attempt to represent the geometry of the propeller explicitly with rotation incorporated. This is much more detailed for representing the complex, swirling jets correctly [20][24][28]. A significant research gap here is that in almost all of the existing literature related to the use of CFD models for scouring, propellers’ geometry for such scouring processes is either entirely disregarded or fixed structures such as piles or pipelines are modeled [1][4][7][10]. This is a significant research gap that suggests that despite evidence of preceding research in the area of numerical models for scouring in general, applications of such models for the peculiar hydrodynamic conditions created by a propeller are still remarkably underdeveloped [9].

From the table produced using numerical methodology (Table 2), it is observed that the research field is in a state of transition, where a trade-off between methodologies is evident. Most of the research is either using actuator disk models with reduced complexity to estimate large-scale sediment transport plumes but with no consideration for bed scour mechanics or using advanced sliding meshes to estimate the rotation of the propeller with models that only account for suspended loads. This state of affairs draws attention to a critical gap in research: there is no integrated approach that is able to couple complex propeller hydrodynamic models with a sophisticated bed scour mechanics framework that can estimate bed-load transport rates and the developed scour hole geometry, implying that despite significant research efforts in various aspects of the issue, a capable CFD-based prediction tool for studying propeller-induced scour seems to remain a promise for the future.

Table 2. Summary of numerical modeling approaches for propeller-induced scour.

Hydrodynamics models coupled with sediment transport models are critical for scour simulations. When it comes to bed-load transport models, models developed by Engelund & Fredsøe, Van Rijn, or Meyer-Peter & Müller are universally coupled with CFD numerical solvers through equations such as the Exner equation for bed change representation [1][3][29][30]. These models are fairly robust for sandy sediments but require calibration for application to sediments with grade or for cohesive sediments [2][4]. When it comes to suspended load transport models, their representation is achieved through a convection-diffusion term with source terms representing entrainment or deposition with calibrated models [7][22][29]. Quite often, researchers who emphasize bed-load transport models ignore suspended transport models, thereby potentially causing a loss of total scour depth or downstream deposits [30]. More complex models include bidirectional models that provide bed geometry information back to the flow solution. While physically more accurate, such models increase computational complexities [4][29].

The finest scale description is that given by the coupled Discrete Element Method (DEM)/CFD model, representing the sediment as discrete elements that interact with the fluid phase as well as with each other [10][19][31]. This is very good for capturing the physics of granular media but is ludicrously expensive in computation, allowing it to be practically used only for small-scale, small-time simulations with simplifications of the grain geometry to mere spheres [31][32]. This means that there is a natural ordering here: Large-scale simulations with transport relations in RANS models for the phenomena, small-scale investigations with Coupled DEM/CFD for the processes.

Propeller scour directly impacts various forms of infrastructure. Quayside walls can become vulnerable to toe erosion by confined jets, potentially undermining structural integrity [5][13][20]. Foundations in the comparatively harsh offshore environment, such as jackets supporting offshore wind turbine platforms, encounter complex scour conditions that are very different from those of monopiles, with both local pile scour and global scour beneath the platform [7][33][34]. Submarine pipelines can become prone to free spanning as a result of local erosion, making fatigue a possibility [26].

As for testing, empirical equations like the ones suggested in the PIANC guidelines (2015) are used by engineers. Nevertheless, it is observed in various research studies that such equations, developed using data from monopile structures, can be unreliable for other cross-sections [2][8][20]. Improved equations with important parameters such as wall clearance were suggested by Macías-Lezcano et al. [22] among other researchers. A major flaw is that these equations are developed using laboratory data for uniform sands. Their application in real environments with cohesive or graded sediments, complex loading, or complicated cross-sections is still dubious.

Successful risk management requires a diversified approach. Structural methods of risk reduction include riprap armor work, concrete mattresses, and aprons. Chen et al. [18] used their research to quantify the effectiveness of riprap with respect to jacket foundations, concluding that it could lower scour depth by approximately 80% in clear-water scour, although its effectiveness decreases with live bed scour. One important lesson from such research is that protection must be designed for sufficient depth and area to prevent edge scour. A primary limitation of structural solutions is their substantial upfront capital and installation cost, alongside ongoing maintenance requirements in a dynamic marine environment.

Additionally, operational measures are often the earliest forms of defense. These measures include minimizing propeller revolutions per minute during critical maneuvers, using tug support to minimize the thrust of the principal propeller in proximity to infrastructure, and improving docking maneuvers [25][27][35]. Castells-Sanabra et al. [21] showed that other methods of conducting maneuvers could potentially lower scour by up to 80%. Simulation of ship maneuvers with hydrodynamic models has been used to visualize real-time scour risk [27]. However, the effectiveness of operational measures can be constrained by practical requirements for port efficiency, safety protocols, and the need for coordination between vessel crews and port authorities, which may limit their consistent application.

In many cases, the most robust and economical solution is an integrated one that takes into account bed protection strategies such as targeting the quay toe, as well as other operational measures. An important research area that is still missing in the literature is the cost-benefit analysis of various portfolios of measures in terms of their lifetime cost, which would be of great use for the engineer/designer.

These inherent uncertainties are pushing the need for probabilistic risk models. A study by Kim et al. [36] introduced a procedure for determining the ultimate limit state reliability of the foundation with respect to the risk of scour, taking into consideration the uncertain parameters of environmental loads and scour prediction. This helps in more rational design, as it is based on reliability, unlike the use of arbitrary safety factors.

The key to the future of scour prediction is the coupling of monitoring systems with prediction models. This is where “digital twins”, or real-time models of physical systems updated with real-time data from sensors, promise to be an important new approach [37]. In practice, such a system would function by continuously integrating field measurements—for instance, bathymetric data from multi-beam sonar—into a calibrated predictive scour model, enabling the real-time updating of risk assessments for critical infrastructure. Real-time bathymetric monitoring is one method of tracking scour development. While their application is intriguing, it is important to note that monitoring-prediction systems are still in their infancy with regard to their application in engineered systems.