ebooks in fluid mechanics

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Summary

Introduction

Ambitious wind power development programs were launched by many countries to promote the exploitation of renewable energy and a significant part of the expansion will occur in the form of offshore wind farms (Danish Energy Authority 2005). In Denmark, for example, 28 per cent of the electricity is now produced from wind, and the figure is predicted to reach 50 per cent by 2020 which means the current capacity will be extended by 2000 MW wind power before 2020, and 1500 MW will come from offshore wind farms.

The foundation of an offshore wind turbine, which transfers the forces from the structure to the surrounding soil, is a critical part in the design of a wind turbine structure and it may account for up to 35 per cent of the total installed cost (Byrne & Houlsby 2013). The foundation options usually are gravity-based foundations and monopiles for shallow water, suction caissons and multiple-footing foundations for relatively deep water, and floating options for much deeper water (Breton & Moe 2009).

Linton & Evans (1990) made major simplifications to the calculation of forces and free-surface amplitudes and exploited the exact theory for the scattering of waves by N vertical circular cylinders developed by Spring & Monkmeyer (1974). Subsequently, many theoretical studies in terms of wave–vertical pile interactions were carried out (Evans & Porter 1997; Malenica, Taylor & Huang 1999; Li, Zhang, Guan & Lin 2013). Recently, Liu, Li & Li (2007) experimentally investigated the group effectiveness and the effect of superstructures on wave current forces. Research on the response of offshore foundations to cyclic loads such as wave loadings has been conducted over the past few decades, and a series of two-dimensional (2D) and three-dimensional (3D) models have been developed to obtain a better understanding of the interactions between soil and pile foundations (Randolph 1981; Yang & Jeremic 2002). However, pore-water pressures have been left out of the preceding works and the soil was considered a material without voids. In addition, engineers tend to increase pile stiffness or soil ultimate bearing capacity to avoid foundation failure. As a matter of fact, pore-water pressure that accumulates in the wave-action process may lead to a decrease of effective stress and eventual collapse of the upper structure.

Summary

Introduction

The co-existence of waves and currents in offshore areas is a common physical phenomenon and their interaction is an important topic in coastal and ocean engineering. The presence of a current in a propagating wave will change the original characteristics of wave. For example, the following current will elongate the wavelength, and the opposing current will shorten the wavelength. However, most previous studies of the soil response in marine sediments have considered wave loading only. In fact, the pressure acting on the seabed is significantly different when there is a current in the flow field, according to the potential flow theory. In Hsu et al.'s (2009) work, the thirdorder approximation for wave-seabed interactions was used to determine the dynamic pressures acting on the seabed surface for the porous seabed model. Later, the same analytical solution for wave-current interactions (Hsu et al. 2009) was used to develop analytical solutions based on the quasi-static approximation (Zhang, Jeng, Gao & Zhang 2013), the u–p approximation (Liu et al. 2014) and the u–U approximation (Liao, Jeng & Zhang 2015). A similar approach was adopted to examine the case of a fully buried pipeline (Wen, Jeng & Wang 2012).

In this chapter, the theoretical models of wave-current interactions are outlined first. Then the effects of currents on the oscillatory seabed response are investigated numerically by adopting the ‘u–p’ approximation (Biot 1956a; Zienkiewicz et al. 1980), in which the inertial terms of solid and pore fluid are both considered as the governing equations for a porous seabed. Based on the numerical model, the effects of current on seabed response are investigated; a parametric study is carried out to investigate the effects of wave and soil characteristics on the seabed response, as well as the liquefaction under combined loading of non-linear waves and currents.

Flow Models for Wave-Current Interaction

Analytical Solution: Third-Order Approximation of Wave-Current Interactions

In this chapter, to obtain more accurate results of seabed response under combined wave and current loadings, the third-order solution of wave-current interactions is used to determine the dynamic wave pressures acting on the seabed. For the problem of the third-order wave-current interactions, some works are available in previous literature. The interaction between a linear wave and a uniform current was studied by Thomas (1981). Baddour & Song (1990b) further investigated the interaction of linear waves and currents.

Opening with recent advances in both the theoretical and physical models for wave-seabed-structure interactions, this book provides an updated look at the mathematics behind the interactions between sea, soil and man-made structures. The main models are broken down into key equations, and their strengths and challenges are discussed. These models are then placed in context with industry-relevant examples, in both two and three dimensions. From seabed instability around offshore wind turbines, to soil conditions in response to the laying of submarine pipelines, this book takes a comprehensive look at a variety of wave-seabed-structure interactions. With important implications for the future of offshore infrastructure, this is an ideal resource for industry workers, undergraduate students, and researchers.

Summary

The phenomenon of the wave-seabed-structure interaction has attracted extreme attention among coastal and geotechnical engineers in recent years. Intensive research activities in the area have been carried out by numerous research groups across the world. Understanding of the mechanisms and processes of the wave-seabed-structure interaction problem is particularly important for marine geotechnical engineers involved in the design of foundations around marine infrastructures. The aim of this book is to provide readers with a comprehensive theoretical background for the wave-induced soil response in marine sediments around marine infrastructures, covering various aspects.

This book consists of eight chapters. The first chapter sets out the background to the topic, describes recent advances in the area and explores possible future research agendas. This chapter is a useful starting point for postgraduate students, and provides junior researchers and readers new to this discipline with an overall picture of the research topic. Chapter 2 presents detailed mathematical formulations for the wave-induced soil response, including pore pressure, effective stresses and soil displacements. This chapter summarises the key processes from my first book (Porous Models for Wave-Seabed Interactions, published by Springer in 2013) and some additional new results. Chapter 3 presents analytical and numerical models for the seabed response subject to combined wave and current loading. In Chapters 4 and 5, two-dimensional marine infrastructures are considered. Among these, seabed response around caisson-type breakwaters is presented in Chapter 4. The cases of a submerged breakwater and a breakwater on a sloping seabed are included in the chapter. In Chapter 5, offshore pipelines are considered, including those fully and partially buried in a trench layer. In Chapters 6 and 7, three-dimensional model are presented for two different types of marine infrastructures: breakwaters and offshore wind turbine foundations. Chapter 6 provides an intensive study for the soil response around breakwater heads, while Chapter 7 presents the case of conventional offshore wind turbine foundations such as monopiles and a case study at Donghai offshore wind farms. Finally, Chapter 8 presents results of the recent laboratory experiments on the wave-induced oscillatory pore pressures, including sand-clay mixtures.

Summary

Introduction

Considerable efforts from researchers in the field of marine geotechnics have been devoted to the phenomenon of the wave-induced soil response since the 1970s. One reason for the growing interest is that many coastal/offshore structures (such as vertical walls, caissons, offshore monopiles and pipelines) have been damaged by the waveinduced seabed response, rather than from construction deficiencies (Christian et al. 1974; Smith & Gordon 1983; Lundgren et al. 1989).

As mentioned in Chapter 1, two mechanisms of the wave-induced soil response have been reported in the literature. Both oscillatory (transient) and residual mechanisms of the wave-induced soil response have been intensively studied since the 1970s with two different approaches: the Yamamoto–Madsen model (Madsen 1978; Yamamoto et al. 1978) for the oscillatory mechanism and the Seed–Rahman model (Seed & Rahman 1978) for the residual mechanism. Following these approaches, numerous models have been proposed in the literature. In this chapter, the basic concepts and some key results of the previous models for wave-seabed interaction will be summarised.

Oscillatory Mechanism

Basically, previous studies of the wave-induced oscillatory soil response can be classified into three categories: the Yamamoto–Madsen model, the boundary-layer approximation and the dynamic model. We outline the contribution of several key publications available in the literature here.

Summary

Introduction

Breakwaters are commonly adopted to protect and enhance the utility of coastlines. For example, the total length of all breakwaters in Japan is 4,143 km – one-fifth of its coastline (Hsu, Uda & Silvester 2000). In countries such as the United Kingdom and Japan, coastline protection is a national priority. The construction of new breakwaters and the expansion of existing breakwaters involve major investment. Worldwide, the combined costs for building new breakwaters and maintaining the existing ones are on the order of tens of billions of pounds a year.

Breakwaters are vulnerable to liquefaction of the seabed foundation, a process that can often lead to significant degradations of the foundation in as little as a few years after construction and can sometimes even result in total collapse (Zen et al. 1985; Lundgren et al. 1989; Franco 1994; Zhang & Ge 1996; Sumer & Fredsøe 2002; Chung, Kim, Kang, Im & Prasad 2006). Inappropriate design or maintenance of breakwaters can lead to catastrophic coastal disaster. A recent example of coastal tragedy caused by the failure of breakwaters is that of New Orleans during Hurricane Katrina, which caused deaths and personal and economic chaos (Travis 2005).

The phenomenon of wave-seabed-structure interactions (WSSIs) has a major bearing on this issue and is central to the design of coastal structures such as breakwaters, pipelines and platforms. There have been numerous investigations of wave-seabed interactions around marine structures based on Biot's poro-elastic theory. Among these, Mase et al. (1994) developed a finite element method (FEM) numerical model to investigate wave-induced pore-water pressures and effective stresses under standing waves in a sand seabed and in the rubble-mound foundation of a composite caisson-type breakwater based on Biot's consolidation equations. Later, Mizutani & Mostafa (1998) and Mostafa et al. (1999) developed a boundary element method–FEM combination numerical model to investigate the wave-seabed-structure interaction. In their models, Poisson's equation is used to govern the irrotational wave field for an incompressible, inviscid fluid, and Biot's poro-elastic consolidation equations are used to govern the porous seabed and structures. Jeng, Cha, Lin & Hu (2001) developed a two-dimensional (2D) generalised FEM numerical model (GFEM-WSSI) to investigate the wave-induced pore pressure under a linear wave around a composite breakwater located at a finite, isotropic and homogeneous seabed.

The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. This textbook, fully revised and enlarged for the second edition, presents the minimum of what every physicist, engineer and mathematician needs to know about hydrodynamics. It includes new illustrations throughout, using examples from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, and geophysical and astrophysical phenomena, providing readers with a better understanding of the world around them. Aimed at undergraduate and graduate students as well as researchers, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains forty-one original problems with very detailed solutions, progressing from dimensional estimates and intuitive arguments to detailed computations to help readers understand fluid mechanics.

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7 - Seabed Instability around Offshore Wind Turbine Foundations

Summary

3 - Soil Response in Marine Sediments under Combined Loading of Waves and Currents

Summary

Mechanics of Wave-Seabed-Structure Interactions

Preface

Summary

Appendix E - Mathematical Model of the Two-Layered Viscous Fluid System (Liu et al. 2009)

Appendix A - Analytical Solution for a Seabed of Finite Thickness (Hsu & Jeng 994)

References

2 - Basic Seabed Mechanisms

Summary

Author Index

Subject Index

Frontmatter

4 - Integrated Model of Wave-Seabed Interactions around Caisson-Type Breakwaters

Summary

Frontmatter

Contents

Epilogue

3 - Dispersive waves

Fluid Mechanics

Preface to the Second Edition

Index

4 - Solutions to exercises

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Summary

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Mechanics of Wave-Seabed-Structure Interactions

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Fluid Mechanics