# Modelling waves and their impact on moored ships

Research output: ThesisDissertation (TU Delft)

### Abstract

Ships that are moored at a berth in coastal waters are subject to various external forcings, including the hydrodynamic loads that are induced by the local wave field.
If the ship motions resulting from these wave-induced loads become too large, they may hamper safe operations (e.g., the loading of a container ship). Accurate predictions of the hydrodynamic loads are therefore desired to ensure safe operations of moored ships.

In a coastal environment, the wave field is generally dominated by short waves. The majority of these waves originate from the open ocean, where they are generated by the wind. If the short waves are energetic at a berth, they may cause a significant response of a moored ship. In addition, nonlinear wave effects can excite significant ship motions, which may even occur during relatively calm wave conditions or in a region that is sheltered from energetic short waves. This significant response is primarily related to the presence of infragravity waves, which are excited through nonlinear interactions amongst pairs of short waves.
An accurate description of this nonlinear wave field is therefore indispensable when predicting the hydrodynamic loads that act on a ship which is moored in coastal waters.

The range of scales and physical processes involved in such studies make this a challenging problem to solve using numerical models.
At present, the existing models that can predict the wave impact on a moored ship based on an offshore wave climate are restricted to relatively mild wave conditions.
This thesis set out to develop a new modelling approach to advance our capabilities in solving this complex problem.
The proposed model aims to be applicable at the scale of a realistic coastal or harbour region (say in the order of $1 \times 1$ km$^2$), while accounting for the relevant physical processes. This includes the processes that govern the nonlinear wave evolution over a varying bottom topography (e.g., the nonlinear interactions that excite infragravity waves), and the interactions between the waves and a moored ship (e.g., the scattering of waves by a fixed floating body). The approach is based on the recently developed non-hydrostatic wave-flow model SWASH, which has been successfully applied to simulate a range of wave related processes. This work pursues the development of a new modelling approach through a further development and evaluation of the SWASH model in (i) simulating the nonlinear wave dynamics in a coastal region, and (ii) simulating the interactions between waves and a restrained ship.

The first crucial step in this development is to determine if the model can resolve the nonlinear wave field in a coastal environment. Previous studies showed that models like SWASH can resolve the short-wave dynamics in coastal waters. However, they did not address if such models can resolve the dynamics of the infragravity-wave field. Furthermore, most of these studies focussed on laboratory applications due to computational limitations, whereas field scale applications of non-hydrostatic models have been rarely reported. With the ever increasing computational capabilities, such scales are now within the reach of the state-of-the-art computer systems. To advance the capability of the non-hydrostatic approach towards such realistic applications, this work presents a thorough evaluation of the SWASH model in resolving the nonlinear wave dynamics at the scale of a realistic coastal region. Given the importance of infragravity waves with respect to the wave-induced response of a moored ship, this work particularly determines if the model can resolve their nearshore evolution.

The model was validated using both laboratory and field experiments, covering a range of wave conditions (varying from bichromatic waves to short-crested sea states). A comparison between model predictions and laboratory measurements showed that the model captures the frequency dependent cross-shore evolution of infragravity waves with a coarse vertical resolution (2 layers), including their steepening and eventual breaking close to the shoreline. These results demonstrate that the model can efficiently resolve the dominant processes that affect their nearshore evolution (e.g., nonlinear interactions, shoreline reflections, and dissipation), permitting applications at the scale of a realistic harbour or coastal region.

To determine the capability of the model at such scales, SWASH was applied to study the infragravity wave dynamics at a field site near Egmond aan Zee (the Netherlands), which is characterised by a complex bottom topography. The model was used to reproduce a total of six sea states (including mild and storm conditions), which were measured as part of a two month field campaign. For all conditions, the predicted wave field gave a good representation of the natural conditions, supporting a further study into the infragravity wave dynamics. A unique feature of these predictions is their extensive spatial coverage, allowing analyses of the wave dynamics at scales not easily covered by in-situ measurement devices.
Amongst others, this study showed that a significant portion (up to 50%) of the infragravity wave motion can be trapped at a nearshore bar. This shows the potential of the model to improve our understanding of such complex wave dynamics.

The findings of the flume and field studies further show that the SWASH model provides a powerful tool to predict the nonlinear wave field at a coastal berth based on an offshore wave climate. To predict the impact of this wave field on a ship that is moored at such a berth, the next crucial step in the model development is to account for the interactions between the waves and a restrained ship. For this purpose, a fixed floating body was schematised within SWASH. The model was validated by comparing model results with an analytical solution, a numerical solution, and two laboratory experiments that consider the wave impact on a restrained ship for a range of wave conditions (varying from a solitary wave to a short-crested wave field). These comparisons showed that the model captures the scattering of waves, and the hydrodynamic loads that act on the body. Remarkably, a coarse vertical resolution sufficed to resolve these dynamics. This shows the potential of the model in efficiently simulating the wave-ship interactions.

The findings of this thesis demonstrate that, with the inclusion of a fixed floating body in SWASH, a novel modelling approach has been developed that can efficiently resolve the key dynamics that govern the nearshore evolution of waves and their interactions with a restrained ship. Although further work is required, for example, accounting for the motions of a moored ship, this demonstrates the approach has the potential to simulate the wave-induced response of a ship that is moored in coastal waters. This thesis thereby sets the stage to advance our modelling capabilities towards such realistic applications in a complex coastal environment.
Original language English Doctor of Philosophy Pietrzak, J.D., SupervisorZijlema, M., Supervisor NWO 14 Sep 2016 https://doi.org/10.4233/uuid:c34395a2-43c8-44f2-bc13-01d42bec992e Published - 2016