The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

This article reviews Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles by P. A. Martin , 2006. 450 pp. Price: $140.00 (hardcover). ISBN: 0-521-86554-9

Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles

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Performance of twin-pontoon floating breakwaters

Tender-assisted drilling (TAD) has been revealed as an efficient and effective solution in deep water installations to support drilling operations of tendon leg platforms (TLP). Although this concept is new in offshore Brazil, this has been used for more than 30 years not only in the Southeast Asia but also in the Gulf of Mexico, West Africa, and the North Sea. Due to the complex scenario of two floaters moored in close proximity, an extensive and careful hydrodynamic analysis is required to guarantee a successful execution. This work presents a numerical study of coupled wave motions on the TLP–TAD multibody system with the aim of investigating first-order loads, mean drift loads, and wave frequency responses using frequency and time domain approaches. Hydrodynamic coefficients were calculated by the 3D diffraction–radiation panel method; the mooring systems and the mechanical connection between the floaters were modeled through stiffness matrixes. In frequency domain analysis, several relative positions between the floaters were considered. On the other hand, in time domain studies, the finite element method (FEM) was used to represent moored systems and mechanical connections between the floaters. FEM allows the inclusion of drag forces, added mass, and interactions between mooring lines and floaters into the nonlinear dynamic simulations.

Coupled wave motions on a tension leg platform and tender-assisted drilling

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

Interaction of water waves and floating twin cylinders in beam waves

The dynamic responses of twin bodies with or without connections under the action of beam waves are discussed. The boundary integral method is employed to calculate the velocity potentials of fluid. Effort has been made to reduce the computing time of the Green function and its normal derivative on the body surfaces. The dynamic equations of a single cylinder or twin cylinders in the frequency domain are solved numerically. The irregular frequencies for twin bodies are discussed. In order to find some regularity in the interaction between waves and the twin bodies, a systematic calculation for different parameters such as different stiffness of connections and different distances between the two bodies, different water depths etc., are performed. The calculated responses for a single half-circular cylinder are compared with the experiments performed in a wave flume and were in very good agreement. The dynamic responses of twin half-circular cylinders with connections of different stiffness have been calculated and also compared with the experiments carried out in the wave flume. The calculated responses of the heave of the twin bodies coincide with the measurements. The effects of different stiffness, different distances between the two bodies and different water depths on the responses are discussed.

Shuangwu Chen

Papers

Interaction of water waves and floating twin cylinders in beam waves

Dynamic responses of floating twin bodies in beam waves