In this research, a systematic breakdown of different phenomena is conducted to study in detail the response of moving objects in realistic muddy environments. As a starting point, a review of the existing literature related to navigation in muddy environments and its modelling is included. Then, the examination of various approaches used to account for the influence of the rheological properties of mud layers is investigated, with a particular focus on experimental works and theoretical models. Subsequently, phenomena found in nature that are related to interactions with internal waves are also investigated. Finally, the combination of all these different phenomena is analysed, giving an initial estimation and a solid background of what could be expected in muddy environments. This comprehensive review forms the foundation for understanding the complexities of mud dynamics and its potential influence on the response of moving objects. 

To measure the influence of natural mud in the hydrodynamic forces acting on floating bodies, a series of towing experiments were conducted with two different geometries. These experiments were conducted in various fluid combinations, including freshwater, natural mud, and a two-layer fluid system of seawater over natural mud, to replicate a muddy environment. The seawater and natural mud used in this work were obtained from the Port of Antwerp-Bruges (formerly Port of Zeebrugge) in the Zeebrugge harbour area in Belgium.

Due to the inherent complications of towing experiments with ship models in muddy environments,  a more pragmatic approach was adopted in this work by using two simplified geometries as towed objects. To study the mud responses under different fluid flow scenarios, two distinct experimental arrangements were designed. In the first set of towing experiments, a horizontal cylinder that would generate a predominantly 2D flow was tested. The towing velocity range was kept at low length-based Froude numbers in order to have a small free surface deformation in which the 2D flow assumption can hold. For the second experimental campaign, the towed object was a surface-piercing hydrofoil that generated a 3D flow field. In this case, the tested velocity range was significantly higher compared to the first set of tests. The different hydrodynamic forces acting on the body were recorded with high-end instrumentation in the experimental facilities of Flanders Hydraulics in Antwerp, Belgium.

During the experiments, a significantly different response of the natural mud layer on the objects in both experimental campaigns was observed. Moreover, the presence of the natural mud had a significant influence on the hydrodynamic forces acting on the passing bodies. Depending on different kinematic and environmental conditions, the recorded hydrodynamic forces displayed substantial increments when compared to measurements in freshwater cases. One of the main contributors to the overall forces was found to be the viscoplastic properties of the natural mud, which was more significant in cases when the moving objects were initially partially submerged within the mud layer.

Additionally, for the case of the horizontal cylinder, at a certain towing velocity, an internal undulation with a behaviour similar to an internal hydraulic jump, named false hydraulic jump, was observed. This false hydraulic jump had a significant influence on the recorded forces acting on the cylinder. On the other hand, this false internal jump did not have a significant influence on the surface-piercing hydrofoil because of the slenderness of the geometry and the towing velocity range, being much larger than the critical velocities. 

Only a few studies are available in the literature that could be used as validation material for nautical applications. The different results presented in this work can be valuable validation data for the development of new numerical models. It also gives an idea of which rheological properties—and under which conditions—must be included to adequately describe navigation in muddy environments.

In maritime applications, one of the most common methods to model fluid-related phenomena is Computational Fluid Dynamics (CFD). In muddy environments, under the assumption that the natural mud layer is a continuum, it is possible to incorporate complex rheological properties, offering a reasonable approximation of reality. In literature, a few CFD studies related to muddy environments have shown promising results in replicating the response of ships in these conditions. Given the intrinsic challenges involved in modelling the rheological properties of natural mud, it is often simplified as either a Newtonian or a Bingham fluid. However, it is essential to note that these models do not account for the time-dependent behaviour of mud under accelerating or decelerating conditions. Therefore, further validation efforts are crucial to assess the accuracy and reliability of CFD models in these conditions.

In this work, CFD simulations were conducted to replicate the two experimental campaigns. Numerical computations using available solvers and libraries yielded different levels of accuracy for each evaluated condition. For 3D simulations, the overall forces for the whole velocity range were fairly well replicated using the proposed numerical method. On the contrary, simulations assuming a 2D flow demonstrated a significant deviation of the computed forces when compared with experimental measurements.

The disparity between the two simulation cases can be attributed to many reasons. One of the primary issues is that the numerical setup proposed in this work does not correctly replicate conditions with strong instabilities in the water-mud interface. This problem can be closely related to the way the natural model is described. Many phenomena, such as mixing, stratification, and time-dependent properties, are not included in the modelling. Moreover, the turbulence model used in this work does not include corrections or additional treatments for non-Newtonian properties, which could be essential for the proper description of the water-mud interface and, consequently, the hydrodynamic forces acting on floating objects. In any case, the proposed numerical setup is an initial motivation for further development of more sophisticated representations of the natural mud for nautical applications.