Abstract:
Since long, oceans have been serving mankind in various ways and of course, at the same time the waves have also shown their fury at times by claiming lives and creating huge destruction. In order to understand the oceans and the strength they display through waves, it becomes very pertinent to study ocean waves, their behaviour and effects with respect to wave propagation, scattering, damping, trapping etc., which influence a number of issues in connection with marine structures and coastal regions. The comfortable situation to work with ocean waves is by considering simple conditions thereby neglecting many important aspects such as the porosity of the structures that are installed in ocean for various activities, porous and elastic effects of the sea-bed and also the unevenness of the sea-bed. However, the real situation demands that some or all of these be taken into account while modelling a problem so that the problem is formulated for a more realistic scenario.
In order to reduce the wave impact on marine structures (i.e., to dissipate the wave effects), it is essential that the structures (such as cylinders, barriers, caissons) possess in them the ability to reflect the wave and help in attenuating the wave energy. This brings into fore the utility of porous structures which can be used as breakwaters in the coastal and offshore regions for various applications. Further, it is practically impossible to find sea-beds which are flat and do not possess any porosity or elasticity. In other words, a more realistic formulation can be carried out by considering structures possessing porosity, and sea-beds being uneven and possessing porosity and/or elasticity.
The objective of this talk is to discuss scattering of water waves by various types of porous structures placed on flat or uneven sea-bed which may possess porosity and/or elasticity. The study focuses on how reflection varies when different important parameters are changed. The observations made from this study will allow one to design structures which will be effective enough to reduce wave impact on the structures. In this talk, some results will be displayed which portray the physical scenario. An attempt will be made to present some practical problems which take into account a number of important properties and parameters so that the results become practical to be followed by relevant people for various activities with regard to protecting certain regions and structures from harsh ocean wave action. It will mainly emphasize the significant role that porosity and elasticity play with regard to ocean wave propagation and various related issues. The emphasis will be on the modelling of the problems which will establish the essence of mathematics. A brief and friendly introduction to water wave propagation will precede the main components of the talk to give some general idea to the audience.