Interaction of Water Waves with Small Undulations on a Porous Bed in a Two-layer Ice-covered Fluid

The scattering problem involving water waves by small undulation on the porous ocean-bed in a two-layer fluid,is investigated within the framework of the two-dimensional linear water wave theory where the upper layer is covered by a thin uniform sheet of ice modeled as a thin elastic plate.In such a two-layer fluid there exist waves with two different modes,one with a lower wave number propagate along the ice-cover whilst those with a higher wave number propagate along the interface.An incident wave of a particular wave number gets reflected and transmitted over the bottom undulation into waves of both modes.Perturbation analysis in conjunction with the Fourier transform technique is used to derive the first-order corrections of reflection and transmission coefficients for both the modes due to incident waves of two different modes.One special type of bottom topography is considered as an example to evaluate the related coefficients in detail.These coefficients are depicted in graphical forms to demonstrate the transformation of wave energy between the two modes and also to illustrate the effects of the ice sheet and the porosity of the undulating bed.

Reduction of wave impact on seashore as well as seawall by floating structure and bottom topography

The three-dimensional problem involving diffraction of water wave by a finite floating rigid dock over an arbitrary bottom is studied for two cases(1)in the absence of wall(2)in the presence of wall.The problem is handled for its solution with the aid of step method.Here both asymmetric and symmetric arbitrary bottom profile is approximated using successive steps.Step approximation helps to apply the matched eigenfunction expansion method,in result,system of algebraic equations are obtained which are solved to determine the hydrodynamic quantities,namely,force experienced by rigid floating dock as well as rigid seawall,free surface elevation,transmission and reflection coefficients associated with transmission and reflected waves respectively.The effects of various structural and system parameters are examined on these hydrodynamics quantities.The appropriate values of length and thickness of dock,water depth and angle of incidence provide the salient information to marine and coastal engineers to design the offshore structures and creation of parabolic trench on the bottom.The present results are compared with known results in special case of bottom topography.The energy balance relation is derived and checked.