The boundary integral equation method, also known as the method of singularities, is described. The Green function, consisting of Rankine and Kelvin parts, is introduced. Application of Green’s identity leads to an integral equation, which is solved numerically. Numerical aspects are covered, such as how to remedy the problem of irregular frequencies, or include coexisting current.

The hydrostatics in a fluid at rest are described. Such notions as center of buoyancy, metacentric radii, metacentric heights, hydrostatic stiffnesses are introduced.

Distinction is made between shallow water and deep water wave theories, depending on the value of the Ursell number. Potential flow theory is applied and the Stokes development is followed and first-order (linear), second-order, and third-order wave theories, in regular and irregular waves, are described. The concepts of phase and group velocities, mass transport, and energy flux are introduced. The application of stretching models to wave crest kinematics is described. At second-order distinction is made between bound (or locked) wave components (that accompany the first-order wave system) and free components (that travel independently). It is emphasized that, from third-order, such phenomena as mutual modifications of the phase velocities, or exchanges of energy, can take place between wave components. These interactions may lead to the occurrence of rogue waves, or to strong runups often observed at midships. The stream function wave model, which encompasses shallow and deep water cases, is presented. Finally the nonlinear Schr¨odinger equation that describes the time and space evolution of the wave envelope is applied to the prediction of the Benjaminis–Feir instability.

This chapter covers several types of flow instabilities of cylindrical bodies in current: vortex- induced vibrations (VIVs) and galloping, flutter, and wake-induced instabilities (WIO). VIVs mostly affect cylinders of circular cross section and they must be accounted for to assess the fatigue life of risers. The concept of reduced velocity is introduced and illustrative experimental values of VIV responses are given. Predictive methods are briefly described. Galloping instabilities appear at higher values of the reduced velocities for prismatic cylinders. Experimental results are given for a square cylinder and the quasi-static predictive method is outlined. Whereas, in galloping, only one degree of freedom is at hand, in the direction perpendicular to the free stream, in flutter an additional rotational motion comes into play. Finally Wake-Induced Instabilities are described, in the particular case of one circular cylinder in the lee of an upstream one.

The motion of a floating body in waves obeys a damped mass spring equation. The respective roles of mass, damping and stiffness need to be clearly understood. Harmonic and non-harmonic excitations are considered, together with different forms of damping: linear, quadratic, Coulomb.

The concepts of sea state and of short-term and long-term statistics are introduced. Wave by wave and spectral analyses are described; definitions are given of wave spectrum, significant wave height, mean wave period, and narrowness parameter. Theoretical distributions of wave heights (the Rayleigh law) are derived. The concept of return period is introduced. The other environmental parameters considered are the wind, the current, the internal waves, and the marine growth. The different definitions of mean wind velocity are explained. Typical wind profiles and wind spectra are presented.

Illustrated examples are given of marine structures, taken from oil exploitation, floating wind production, and other offshore activities. Important parameters such as the Reynolds number and the Keulegan–Carpenter numbers are introduced and the concepts of large and small (or slender) bodies are defined. The separation between linear and nonlinear wave loads and responses is introduced. Finally a brief outline of the book is given.

The last chapter is devoted to model tests. The basic principles of model testing are first presented, that is the Froude scaling law, and the issued related to the biases in Reynolds number. A review is made of experimental facilities used in ocean engineering, and of the wave generation and absorption principles. Issues related to confinement effects, such as sloshing, seiching, Benjamin-Feir instability, emission of free harmonics, etc., are extensively covered. Recommendations are made on specifications and exploitation of model tests.

In this chapter the wave body interaction is extended to the second order in the wave amplitude. This leads to wave loads, and responses, taking place at the sum and difference frequencies of the components in the incoming wave system. The time averaged wave load (the drift force) is first considered in regular waves. The different formulations of the drift force (near-field, far-field, middle-field, Lagally) are described. The sensitivity of the drift force to a coincident current is emphasized and the extension of the diffraction radiation theory to a superimposed current is presented, together with the so-called Aranha’s formula that offers a practical approximation to the wave drift damping effect. Second-order diffraction theory is detailed in regular waves, with practical application to a bottom-mounted vertical cylinder. The concept of Quadratic Transfer Function (QTF) is first introduced in the case of bichromatic seas and then applied to the low frequency loading in irregular waves, where the validity of frequently used approximations (e.g. Newman approximation) is discussed. A section is then devoted to the Rainey equations which can be viewed as a second-order extension of the inertia term in the Morison equation. Finally practical calculation of the slow-drift and springing responses is considered.

In this chapter linearized potential flow theory is applied to the prediction of wave loads upon marine structures, and of their wave response. The linearized diffraction radiation theory is presented, leading to the wave excitation loads, added masses, and radiation dampings. Analytical, semi-analytical, and numerical methods of resolution are given, the first one for the case of one or several bottom-mounted vertical cylinders. Comparisons are offered with experimental results, where the merits and short-comings of the linearized theory are emphasized. Separate sections are then devoted to specific problems such as barge roll resonance, recovery of wave energy, coupling between seakeeping and sloshing in tanks, and resonances in moonpools and gaps.

The basic equations in fluid mechanics are briefly recalled, starting from the Navier–Stokes equations for an incompressible fluid. Potential flow theory is quickly introduced, together with the generic boundary value problem satisfied by the velocity potential. Applications are made to a few basic cases, such as uniform accelerated flow around a cylinder and the waves generated by a piston wavemaker.