The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of...The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.展开更多
The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here.The boundary condition on the elastic plate is derived from the Bernoulli-Euler equati...The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here.The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate.Using the Green’s function technique,from this boundary condition,the normal velocity of the plate is expressed in terms of the difference between the velocity potentials(unknown)across the plate.The two ends of the plate are either clamped or free.The reflection and transmission coefficients are obtained in terms of the integrals’involving combinations of the unknown velocity potential on the two sides of the plate,which satisfy three simultaneous integral equations and are solved numerically.These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.展开更多
In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or...In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.展开更多
A hydrometeorological study is made of the September, 1900 severe rainstorm which led up to the record rainfalls over Gangetic West Bengal with subsequent disastrous flooding in the Damodar and the Hooghly rivers. The...A hydrometeorological study is made of the September, 1900 severe rainstorm which led up to the record rainfalls over Gangetic West Bengal with subsequent disastrous flooding in the Damodar and the Hooghly rivers. The spatial extent of the rainstorm for different durations has been examined by constructing the isohyetal patterns based on rainfall records of stations affected by the storm. Areal rainfalls for 1,2 and 3-day periods are calculated and the values have been compared with similar values from other major rainstorms of the region. The comparison revealed that the September, 1900 rainstorm was the heaviest for 1,2 and 3-day durations for all the areas. The storm contributed rainfalls of 33.0 cm, 52.0 cm and 62.0 cm over an area of 10,000 km2 in 1,2 and 3 days respectively. This rainstorm could, therefore, be considered as an important input in flood and design storm studies in the Gangetic West Bengal region. A relationship between point to areal rainfall has also been developed with a view to evaluate areal PMP estimates.展开更多
This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely d...This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.展开更多
文摘The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.
基金supported by the NASI Senior Scientist Fellowship project a DST research project (No. SR/S4/MS: 521/08)
文摘The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here.The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate.Using the Green’s function technique,from this boundary condition,the normal velocity of the plate is expressed in terms of the difference between the velocity potentials(unknown)across the plate.The two ends of the plate are either clamped or free.The reflection and transmission coefficients are obtained in terms of the integrals’involving combinations of the unknown velocity potential on the two sides of the plate,which satisfy three simultaneous integral equations and are solved numerically.These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.
文摘In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.
文摘A hydrometeorological study is made of the September, 1900 severe rainstorm which led up to the record rainfalls over Gangetic West Bengal with subsequent disastrous flooding in the Damodar and the Hooghly rivers. The spatial extent of the rainstorm for different durations has been examined by constructing the isohyetal patterns based on rainfall records of stations affected by the storm. Areal rainfalls for 1,2 and 3-day periods are calculated and the values have been compared with similar values from other major rainstorms of the region. The comparison revealed that the September, 1900 rainstorm was the heaviest for 1,2 and 3-day durations for all the areas. The storm contributed rainfalls of 33.0 cm, 52.0 cm and 62.0 cm over an area of 10,000 km2 in 1,2 and 3 days respectively. This rainstorm could, therefore, be considered as an important input in flood and design storm studies in the Gangetic West Bengal region. A relationship between point to areal rainfall has also been developed with a view to evaluate areal PMP estimates.
基金Supported by the DST Research Project No.SR/SY/MS:521/08and CSIR,New Delhi
文摘This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.
