Paramita Maiti

SCATTERING OF OBLIQUE WAVES BY BOTTOM UNDULATIONS IN A TWO-LAYER FLUID

Scattering of waves obliquely incident on small cylindrical undulations at the bottom of a two-layer fluid wherein the upper layer has a free surface and the lower layer has an undulating bottom, is investigated here assuming linear theory. There exists two modes of time-harmonic waves propagating at each of the free surface and the interface. Due to an obliquely incident wave of a particular mode, reflected and transmitted waves of both the modes are created in general by the bottom undulations. For small undulations, a simplified perturbation analysis is used to obtain first-order reflection and transmission coefficients of both the modes due to oblique incidence of waves of again both modes, in terms of integrals involving the shape function describing the bottom. For sinusoidal undulations, these coefficients are plotted graphically to illustrate the energy transfer between the waves of different modes induced by the bottom undulations.

Water waves generated by disturbances at an ice cover

This paper is concerned with two-dimensional unsteady motion of water waves generated by an initial disturbance created at an ice sheet covering the water. The ice cover is modeled as a thin elastic plate. Using linear theory, the problem is formulated as an initial value problem for the velocity potential describing the motion in the liquid. In the mathematical analysis, the Laplace and Fourier transform techniques have been utilized to obtain the depression of the ice-covered surface in the form of an infinite integral. For the special case of initial disturbance concentrated at the origin, taken on the ice cover, this integral is evaluated asymptotically by the method of a stationary phase for a long time and large distance from the origin. The form of the ice-covered surface is graphically depicted for two types of initial disturbances.

On the waves generated due to a line source present in an ocean with an ice cover and a small bottom undulation

In this paper, we study the effect of a small undulation at the bottom of a laterally unbounded ocean covered with an ice sheet, on the waves generated by an oscillating line source submerged in water. A suitable perturbation technique is used for reducing the problem to two independent boundary value problems up to first order. Applying Green’s integral theorem appropriately, the first-order wave amplitude of radiated wave at infinity is obtained in terms of the shape function describing the bottom topography. Particular forms of shape functions are considered, and the corresponding first-order wave amplitudes are evaluated explicitly and depicted graphically. It is observed that for the ocean bottom with a sinusoidal patch, Bragg resonance occurs when the wavelength of the sinusoidal ripple is half the wavelength of the radiated wave at infinity. The study of ocean wave interactions with a thin, floating elastic plate has gained immense importance in recent years as it can be used to model a wide range of physical systems. One of its important applications consists in modelling a very large floating structure (VLFS), that is used in ocean space utilization for the construction of floating airports, offshore runways, etc. Also, a thin elastic plate may be used to model sea ice, which is a thin covering on the ocean surface extending over a large distance. At places of higher latitude, the waves propagating at the free surface of an ocean often interact with a continuous unbroken sheet of ice extending over a large distance. This may occur near a shore, in harbours or bays or may be further out in the sea. As the waves travel beneath the sea ice, the ice-cover plate bends due to its elasticity. If the strain produced is sufficiently large then the ice cover