Executive Summary : | Mathematical study of problems of water wave scattering and radiation is a fascinating and highly interesting topic in applied mathematics as well as in ocean engineering. A large number of applied mathematicians and ocean engineers have contributed significantly, both in terms of developing important mathematical techniques as well as modeling several wave phenomena in ocean (water) which is regarded as incompressible and inviscid fluid. Ever since waves were studied, water waves have served as models for wave theory in general since only water waves can be observed in the naked eye. Consequently the phenomena of wave scattering by obstacles present in water with a free surface have attracted the attention of a number of great mathematicians, physicists and engineers from the nineteenth century. This has resulted in a systematic development of the theory of water waves and has provided a background for a somewhat rich development of various mathematical concepts and techniques. Consequently, the theory of water waves constitutes an important branch of applied mathematics, and due to its vast applicabity in ocean related activities, it has also become an important branch of engineering. In particular the following specific classes of water wave propagation problems will be considered. 1. Wave propagation in the presence of viscoelastic/porous barriers. 2. Wave generation by a moving oscillatory disturbance in presence of porous/elastic bottom or a sloping beach. 3. Wave propagation in the presence of thick barriers and trenches. 4. Radiation and scattering of waves by a submerged circular/ elliptic plate in single, two and three layered fluid: Ocean engineering projects in the deep sea are becoming more relevant with time and the design of ocean platforms is becoming more complicated. A horizontally submerged thin disc is often used in many offshore structures in coastal engineering. 5. Wave propagation problems involving floating rigid dock, floating elastic plates, etc. 6. Water wave diffraction by barrier(s) under an ice-cover with crack. This is a somewhat new topic in the area of water waves and appears to have immense application in coastal engineering. The related mathematical methods involve the use of integral transforms such as Fourier, Laplace, Hankel, Mellin transforms, Green's function theory, singular integral equations, hypersingular integral equations, dual integral equations, perturbation technique, Wiener Hopf technique, Riemann-Hilbert boundary value problem of complex variable theory, Galerkin approximation, the method of matching of eigenfunction expansions etc. Appropriate methods depend on the geometry of the problem considered. |