On linear water wave problem in the presence of a critically submerged body

We study the problem of propagation of linear water waves in a deep water in the presence of a critically submerged body (i.e. the body touching the water surface). Assuming uniqueness of the solution in the energy space, we prove the existence of the solution which satisfies the radiation conditions at infinity as well as, additionally, at the cusp point where the body touches the water surface. This solution is obtained by the limiting absorption procedure. Next we introduce a relevant scattering matrix and analyse its properties. Under a geometric condition introduced by Maz'ya, see \cite{M1}, we show that the method of multipliers applies to cusp singularities, thus proving a new important property of the scattering matrix, which may be interpreted as the absence of a version of "full internal reflection". This property also allows us to prove uniqueness and existence of the solution in the functional spaces $H^2_{loc}\cap L^\infty$ and $H^2_{loc}\cap L^p$, $2<p<6$, provided a spectral parameter in the boundary conditions on the surface of the water is large enough. This description of the solution does not rely on the radiation conditions or the limiting absorption principle. This is the first result of this type known to us in the theory of linear wave problems in unbounded domains

Unsteady hydrodynamics of ships moving in confined waterways

When a ship is navigating on water surface, its resistance can be divided into three components: frictional resistance, eddy resistance, and wave-making resistance (Havelock, 1909). While in many cases, the steady component dominates the wave-making resistance, there are still certain instances where unsteady effects cannot be ignored. For example: • Sudden changes of boundaries, such as the width and depth of the waterway. This may occur when ships navigate in port, harbor or lock environments. It will potentially increase the risk of collisions or grounding incidents. • When a ship is overtaking (or being overtaken) or passing other vessels in busy waterways, the unsteady effects of the free surface can generate horizontal unsteady forces between the two ships. This can result in collisions between the vessels and lead to the blockage of the waterway. • Another typical scenario is when a ship keeps accelerating in open area, particularly in extremely shallow depths. In this case, the unsteady effects will significantly increase after the ship’s velocity exceeds the critical speed. At this point, the unsteady effects alter the flow field around the ship, resulting in changes in wave-making resistance. This thesis posits that the aforementioned unsteady effects are closely correlated with unsteady waves on the free surface. Hence, the primary objectives of this research are two-fold: 1) To develop a linear unsteady numerical program which is capable of simulating the unsteady free surface effects. This program will accurately capture the formation and evolution of unsteady waves. 2) To devise a real-time updating mesh method that handles changes in waterway boundaries and depths encountered during the simulation process. Additionally, it ensures temporal continuity for all cells on the free surface. In this thesis, Chapter 1 will be an introduction and literature review of the research topic. Chapter 2 introduces the methodology used in this research. Chapters 3 to 5 constitute the main body of this thesis. Specifically, Chapter 3 presents the simulation of unsteady waves generated by a single object, with particular focus on the simulation of the previously mentioned scenario of a ship accelerating in shallow water. Chapter 4 aims to simulate multiple objects. In this chapter, the ship-to-ship problem and the unsteady bank effect within a confined waterway will be investigated. Due to the presence of interacting objects, the grid is required to be updated in real-time to accommodate changes in the boundary conditions. The simulation results will be compared with experimental data to validate their accuracy. Chapter 5 will build upon the foundation established in Chapter 3 by extending the grid handling techniques to account for unsteady banks. Additionally, the unsteady hydrodynamic model developed in Chapter 2 will also be incorporated. This integration will enable the simulation of the intricate wave phenomena that occurs during the process of a vessel entering a lock. The simulation results will be compared against experimental data as well as computational fluid dynamics (CFD) results to validate their accuracy. This comparative analysis serves to ensure the reliability and fidelity of the simulation outcomes. By undertaking these efforts, Chapter 4 aims to provide a comprehensive understanding of the wave behaviour within the lock chamber during vessel entry, contributing to the advancement of knowledge in the field of unsteady water dynamics. Finally, Chapter 6 serves as the conclusion which summarizing all the achievements of this thesis and also proposing future directions for research.When a ship is navigating on water surface, its resistance can be divided into three components: frictional resistance, eddy resistance, and wave-making resistance (Havelock, 1909). While in many cases, the steady component dominates the wave-making resistance, there are still certain instances where unsteady effects cannot be ignored. For example: • Sudden changes of boundaries, such as the width and depth of the waterway. This may occur when ships navigate in port, harbor or lock environments. It will potentially increase the risk of collisions or grounding incidents. • When a ship is overtaking (or being overtaken) or passing other vessels in busy waterways, the unsteady effects of the free surface can generate horizontal unsteady forces between the two ships. This can result in collisions between the vessels and lead to the blockage of the waterway. • Another typical scenario is when a ship keeps accelerating in open area, particularly in extremely shallow depths. In this case, the unsteady effects will significantly increase after the ship’s velocity exceeds the critical speed. At this point, the unsteady effects alter the flow field around the ship, resulting in changes in wave-making resistance. This thesis posits that the aforementioned unsteady effects are closely correlated with unsteady waves on the free surface. Hence, the primary objectives of this research are two-fold: 1) To develop a linear unsteady numerical program which is capable of simulating the unsteady free surface effects. This program will accurately capture the formation and evolution of unsteady waves. 2) To devise a real-time updating mesh method that handles changes in waterway boundaries and depths encountered during the simulation process. Additionally, it ensures temporal continuity for all cells on the free surface. In this thesis, Chapter 1 will be an introduction and literature review of the research topic. Chapter 2 introduces the methodology used in this research. Chapters 3 to 5 constitute the main body of this thesis. Specifically, Chapter 3 presents the simulation of unsteady waves generated by a single object, with particular focus on the simulation of the previously mentioned scenario of a ship accelerating in shallow water. Chapter 4 aims to simulate multiple objects. In this chapter, the ship-to-ship problem and the unsteady bank effect within a confined waterway will be investigated. Due to the presence of interacting objects, the grid is required to be updated in real-time to accommodate changes in the boundary conditions. The simulation results will be compared with experimental data to validate their accuracy. Chapter 5 will build upon the foundation established in Chapter 3 by extending the grid handling techniques to account for unsteady banks. Additionally, the unsteady hydrodynamic model developed in Chapter 2 will also be incorporated. This integration will enable the simulation of the intricate wave phenomena that occurs during the process of a vessel entering a lock. The simulation results will be compared against experimental data as well as computational fluid dynamics (CFD) results to validate their accuracy. This comparative analysis serves to ensure the reliability and fidelity of the simulation outcomes. By undertaking these efforts, Chapter 4 aims to provide a comprehensive understanding of the wave behaviour within the lock chamber during vessel entry, contributing to the advancement of knowledge in the field of unsteady water dynamics. Finally, Chapter 6 serves as the conclusion which summarizing all the achievements of this thesis and also proposing future directions for research

Fluid mechanics of waste water disposal in the ocean

Outfall pipes into the ocean are analogous to chimneys in the atmosphere: they are each intended for returning contaminated fluids to the environment in a way that promotes adequate transport and dispersion of the waste fluids. A waste-water treatment plant and an adjoining outfall constitute a system for environmental control; it is practically never feasible to provide such complete treatment that an outfall is not necessary, nor is it common to depend entirely on an outfall with no treatment. Although outfalls and chimneys are functionally similar, there are important differences in their relationships to the coastal waters and atmosphere respectively. Urban and industrial areas, generating waste water, are located along the shallow edge of the ocean, with often tens or even hundreds of kilometers of continental shelf between the shoreline and the deep ocean. The bottom slope on the shelf is typically less than one percent. Thus outfalls extending several kilometers offshore discharge into a body of water of large lateral extent compared to the depth, and are still remote from the main body of ocean water. In contrast, most atmospheric contaminants are introduced at the base of the atmosphere and circulate throughout the whole atmosphere much more readily. Vertical convection mixes the troposphere rapidly in most places and the wind systems circulate the air around the globe in a matter of weeks. Outfalls and chimneys are useful in reducing pollutant concentrations only locally. Far away from the sources, it makes little difference how the pollutants are discharged. The decay times of the pollutants are important in the choice of effective discharge strategies. For example, the problems of very persistent contaminants such as DDT cannot be alleviated by dispersion from an outfall; such pollutants must be intercepted at the source and prevented from entering the environment. On the other hand, degradable organic wastes, as in domestic sewage, may be effectively disposed of through a good ocean outfall. Since the decay time is only a few days, potential problems are only local, and not regional or global

Nonlinear hydrodynamic modelling of wave energy converters under controlled conditions

One of the major challenges facing modern industrialized countries is the provision of energy: traditional sources, mainly based on fossil fuels, are not only growing scarcer and more expensive, but are also irremediably damaging the environment. Renewable and sustainable energy sources are attractive alternatives that can substantially diversify the energy mix, cut down pollution, and reduce the human footprint on the environment. Ocean energy, including energy generated from the motion of wave, is a tremendous untapped energy resource that could make a decisive contribution to the future supply of clean energy. However, numerous obstacles must be overcome for ocean energy to reach economic viability and compete with other energy sources. Energy can be generated from ocean waves by wave energy converters (WECs). The amount of energy extracted from ocean waves, and therefore the profitability of the extraction, can be increased by optimizing the geometry and the control strategy of the wave energy converter, both of which require mathematical hydrodynamic models that are able to correctly describe the WEC- uid interaction. On the one hand, the accuracy and representativeness of such models have a major in uence on the effectiveness of the WEC design. On the other hand, the computational time required by a model limits its applicability, since many iterations or real-time calculations may be required. Critically, computational time and accuracy are often mutually contrasting features of a mathematical model, so an appropriate compromise should be defined in accordance with the purpose of the model, the device type, and the operational conditions. Linear models, often chosen due to their computational convenience, are likely to be imprecise when a control strategy is implemented in a WEC: under controlled conditions, the motion of the device is exaggerated in order to maximize power absorption, which invalidates the assumption of linearity. The inclusion of nonlinearities in a model is likely to improve the model's accuracy, but increases the computational burden. Therefore, the objective is to define a parsimonious model, in which only relevant nonlinearities are modelled in order to obtain an appropriate compromise between accuracy and computational time. In addition to presenting a wider discussion of nonlinear hydrodynamic modelling for WECs, this thesis contributes the development of a computationally efficient nonlinear hydrodynamic model for axisymmetric WEC devices, from one to six degrees of freedom, based on a novel approach to the nonlinear computation of static and dynamic Froude-Krylov forces

A three-dimensional technique for predicting first-and second-order hydrodynamic forces on a marine vehicle advancing in waves

This thesis presents theoretical formulations and numerical computations for predicting first- and second-order hydrodynamic forces on a marine vehicle advancing in waves. The theoretical formulation starts with the derivation of the governing equations for the boundary-value problem of potential flow and its consequence leads to linearised radiation and diffraction problems using the peturbation expansion technique. Solutions of these two problems are obtained by solving the three-dimensional Green function integral equations over the mean wetted body surface. The forward speed free surface Green function representing a translating pulsating source potential for infinite water depth and finite water depth is derived using double Fourier transformation technique. This source potential reduces to an oscillating source at zero speed or to a Kelvin source at zero frequency. In order to solve the three-dimensional Green function integral equations efficiently, symmetry properties of the Green function and the body surface are exploited in the numerical implementation. Using a fully submerged ellipsoid and a half-submerged ellipsoid as examples, the free surface and forward speed effects on hydrodynamic coefficients are investigated. Their cross coupled hydrodynamic coefficients calculated by the present theory satisfy with Timman-Newman relationships. Numerical results for the first-order hydrodynamic coefficients, the wave excitation loads and the resulting motion responses of surface ships are presented. For zero speed case excellent correlations between the calculated and experimental results are found. For the forward speed case, the three-dimensional translating pulsating source modelling and three-dimensional oscillating source modelling with simple speed corrections on the linearised body boundary condition for pitch and yaw motions are used for a realistic ship. When the calculated results are compared with available experimental data, the three-dimensional translating pulsating source, modelling gives better correlations than the three-dimensional oscillating source modelling. Based on the first-order solutions, the mean second-order forces and moments are obtained by direct integrating second-order pressures over the mean wetted body surface. Using zero speed horizontal drifting forces and mean yaw moment as examples, the predictions of the mean second-order forces and moments are compared with available experimental results and found good agreement. For forward speed case the numerical computations for the added resistances of surface ships in head waves are performed by the three-dimensional translating pulsating source modelling and three-dimensional oscillating source modelling. The performance of the former is much better than the latter in comparison with available experimental results. It is found that the successful prediction of the peak of the added resistance is critically dependent upon the motion response results, especially in pitch. Effects of ship heading, forward speed, water depth on the first-order and second-order hydrodynamic forces are investigated

A Review of Cavitation Uses and Problems in Medicine; Invited Lecture

There are an increasing number of biological and bioengineering contexts in which cavitation is either utilized to create some desired effect or occurs as a byproduct of some other process. In this review an attempt will be made to describe a cross-section of these cavitation phenomena. In the byproduct category we describe some of the cavitation generated by head injuries and in artifical heart valves. In the utilization category we review the cavitation produced during lithotripsy and phacoemulsification. As an additional example we describe the nucleation suppression phenomena encountered in supersaturated oxygen solution injection. Virtually all of these cavitation and nucleation phenomena are critically dependent on the existence of nucleation sites. In most conventional engineering contexts, the prediction and control of nucleation sites is very uncertain even when dealing with a simple liquid like water. In complex biological fluids, there is a much greater dearth of information. Moreover, all these biological contexts seem to involve transient, unsteady cavitation. Consequently they involve the difficult issue of the statistical coincidence of nucleation sites and transient low pressures. The unsteady, transient nature of the phenomena means that one must be aware of the role of system dynamics in vivo and in vitro. For example, the artificial heart valve problem clearly demonstrates the importance of structural flexibility in determining cavitation occurrence and cavitation damage. Other system issues are very important in the design of in vitro systems for the study of cavitation consequences. Another common feature of these phenomena is that often the cavitation occurs in the form of a cloud of bubbles and thus involves bubble interactions and bubble cloud phenomena. In this review we summarize these issues and some of the other characteristics of biological cavitation phenomena

Estimation of nearshore wave transmission for submerged breakwaters using a data-driven predictive model

The functional design of submerged breakwaters is still developing, particularly with respect to modelling of the nearshore wave field behind the structure. This paper describes a method for predicting the wave transmission coefficients behind submerged breakwaters using machine learning algorithms. An artificial neural network using the radial-basis function approach has been designed and trained using laboratory experimental data expressed in terms of non-dimensional parameters. A wave transmission coefficient calculator is presented, based on the proposed radial-basis function model. Predictions obtained by the radial-basis function model were verified by experimental measurements for a two dimensional breakwater. Comparisons reveal good agreement with the experimental results and encouraging performance from the proposed model. Applying the proposed neural network model for predictions, guidance is given to appropriately calculate wave transmission coefficient behind two dimensional submerged breakwaters. It is concluded that the proposed predictive model offers potential as a design tool to predict wave transmission coefficients behind submerged breakwaters. A step-by-step procedure for practical applications is outlined in a user-friendly form with the intention of providing a simplified tool for preliminary design purposes. Results demonstrate the model’s potential to be extended to three dimensional, rough, permeable structures

European Red List of Habitats Part 1. Marine habitats

The European Red List of Habitats provides an overview of the risk of collapse (degree of endangerment) of marine, terrestrial and freshwater habitats in the European Union (EU28) and adjacent regions (EU28+), based on a consistent set of categories and criteria, and detailed data and expert knowledge from involved countries1. A total of 257 benthic marine habitat types were assessed. In total, 19% (EU28) and 18% (EU28+) of the evaluated habitats were assessed as threatened in categories Critically Endangered, Endangered and Vulnerable. An additional 12% were Near Threatened in the EU28 and 11% in the EU28+. These figures are approximately doubled if Data Deficient habitats are excluded. The percentage of threatened habitat types differs across the regional seas. The highest proportion of threatened habitats in the EU28 was found in the Mediterranean Sea (32%), followed by the North-East Atlantic (23%), the Black Sea (13%) and then the Baltic Sea (8%). There was a similar pattern in the EU28+. The most frequently cited pressures and threats were similar across the four regional seas: pollution (eutrophication), biological resource use other than agriculture or forestry (mainly fishing but also aquaculture), natural system modifications (e.g. dredging and sea defence works), urbanisation and climate change. Even for habitats where the assessment outcome was Data Deficient, the Red List assessment process has resulted in the compilation of a substantial body of useful information to support the conservation of marine habitats