In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at larg...In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.展开更多
In the present paper, the effect of a small bottom tmdulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed...In the present paper, the effect of a small bottom tmdulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of non uniform finite depth is investigated. A simplified perturbation technique involving a non dimensional parameter characterizing the smallness of the bottom deformation is applied to reduce the given boundary value problem to two independent boundary value problems upto first order. The first boundary value problem corresponds to the problem of water wave generation due to rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of uniform finite depth. This is a well known problem whose solution is available in the literature. From the second boundary value problem, the first order correction to the wave amplitude at infinity is evaluated in terms of the shape function characterizing the bottom undulation, by employing Green＇s integral theorem. For a patch of sinusoidal ripples at the sea bottom, the first order correction to the wave amplitude at infinity for both the configuration of the barrier is then evaluated numerically and illustrated graphically for various values of the wave number. It is observed that resonant interaction of the wave generated, with the sinusoidal bottom undulation occurs when the ratio of twice the wavelength of the sinusoidal ripple to the wave length of waves generated, approaches unity. Also it is found that the resonance increases as the length of the barrier increases.展开更多
基金Supported by the Department of Science and Technology,Government of India for their financial support of this work through the SERC Fast Track Scheme for Young Scientist(No.SR/FTP/MS-037/2011)
文摘In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.
基金Supported by DST through the Research Project No.SR/SY/MS: 521/08
文摘In the present paper, the effect of a small bottom tmdulation of the sea bed in the form of periodic bed form on the surface waves generated due to a rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of non uniform finite depth is investigated. A simplified perturbation technique involving a non dimensional parameter characterizing the smallness of the bottom deformation is applied to reduce the given boundary value problem to two independent boundary value problems upto first order. The first boundary value problem corresponds to the problem of water wave generation due to rolling oscillation of a vertical barrier either partially immersed or completely submerged in water of uniform finite depth. This is a well known problem whose solution is available in the literature. From the second boundary value problem, the first order correction to the wave amplitude at infinity is evaluated in terms of the shape function characterizing the bottom undulation, by employing Green＇s integral theorem. For a patch of sinusoidal ripples at the sea bottom, the first order correction to the wave amplitude at infinity for both the configuration of the barrier is then evaluated numerically and illustrated graphically for various values of the wave number. It is observed that resonant interaction of the wave generated, with the sinusoidal bottom undulation occurs when the ratio of twice the wavelength of the sinusoidal ripple to the wave length of waves generated, approaches unity. Also it is found that the resonance increases as the length of the barrier increases.
