Wyniki wyszukiwania - Biblioteka Nauki

1

Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap

100%

Dolai P.

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2016

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tom Vol. 21, no. 2

303--322

EN

In this paper, the problem of interface wave scattering by bottom undulations in the presence of a thin submerged vertical wall with a gap is investigated. The thin vertical wall with a gap is submerged in a lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green’s integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical wall present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and a suitable application of multi-term Galerkin approximations. The numerical results of the zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature is observed of first-order reflection coefficient due to multiple interactions of the incident wave with bottom undulations, the edges of the submerged wall and the interface. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.

2

Scattering of internal waves by vertical barrier in a channel of stratified fluid

100%

Dolai P.

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tom Vol. 20, no. 3

471--485

EN

The problem of two dimensional internal wave scattering by a vertical barrier in the form of a submerged plate, or a thin wall with a gap in an exponentially stratified fluid of uniform finite depth bounded by a rigid plane at the top, is considered in this paper. Assuming linear theory and the Boussinesq approximation, the problem is formulated in terms of the stream function. In the regions of the two sides of the vertical barrier, the scattered stream function is represented by appropriate eigen function expansions. By the use of appropriate conditions on the barrier and the gap, a dual series relation involving the unknown elements of the scattering matrix is produced. By defining a function with these unknown elements as its Fourier sine expansion series, it is found that this function satisfies a Carleman type integral equation on the barrier whose solution is immediate. The elements of the scattering matrix are then obtained analytically as well as numerically corresponding to any mode of the incident internal wave train for each barrier configuration. A comparison with earlier results available in the literature shows good agreement. To visualize the effect of the barrier on the fluid motion, the stream lines for an incident internal wave train at the lowest mode are plotted.

3

Interface wave generation in two fluid medium in the presence of running stream

100%

Dolai P.

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2008

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tom Vol. 13, no 3

669-679

EN

In this paper, a problem of two-dimensional wave generation due to initial disturbance at the interface between two superposed fluids wherein the upper fluid of finite height above the interface with a horizontal rigid lid and the lower fluid of finite depth in the presence of a uniform running stream in both the fluids is investigated. Assuming linear theory, the problem is formulated as a coupled initial value problem of the velocity potentials describing the motion in the two fluids. In the mathematical analysis, the Laplace and Fourier transform techniques have been utilized to obtain the interface depression when the initial disturbance at the interface is in the form of a prescribed interface depression or an impulse concentrated at the origin. In both the cases, the interface depression is obtained in terms of an infinite integral which is evaluated asymptotically for large time and distance by the method of stationary phase. The asymptotic forms of the interface depression are depicted graphically in a number of figures. The effect of the upper fluid and the presence of the running stream in both the fluids on the wave motion are discussed.

4

Edge waves over a shelf

63%

Dolai P. , Dolai D. P.

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tom Vol. 24, no. 2

453--460

EN

The problem considered in this paper is the derivation of properties of edge waves travelling along a submerged horizontal shelf. The problem is formulated within the framework of the linearized theory of water waves and Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the dispersion relation for edge waves in terms of an integral. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for the integral and hence to derive the properties of edge waves over a shelf. The numerical results are illustrated in a table and curves are presented showing the variation of frequency of the edge waves with the width of the shelf.

5

Interface wave diffraction by bottom undulations in the presence of a thin plate submerged in lower fluid

63%

Dolai D. P. , Dolai P.

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tom Vol. 15, no 4

1017-1036

EN

The problem of interface wave diffraction by bottom undulations in the presence of a thin vertical plate is investigated in this paper. The plate is submerged in the lower fluid of finite depth with bottom undulations and the upper fluid is of infinite height separated by a common interface. In the method of solution, we use a simplified perturbation analysis and suitable applications of Green's integral theorem in the two fluid regions produce first-order reflection and transmission coefficients in terms of integrals involving the shape function describing the bottom undulations and solution of the scattering problem involving a submerged vertical plate present in the lower fluid of uniform finite depth. For sinusoidal bottom undulations, the first-order transmission coefficient vanishes identically. The corresponding first-order reflection coefficient is computed numerically by solving the zero-order reflection coefficient and suitable application of multi-term Galerkin approximations. The numerical results of zero-order and first-order reflection coefficients are depicted graphically against the wave number in a number of figures. An oscillatory nature of first-order reflection coefficient due to multiple interaction of the incident wave with bottom undulations is observed. The first-order reflection coefficient has a peak value for some particular value of the ratio of the incident wavelength and the bottom wavelength. The presence of the upper fluid has some significant effect on the reflection coefficients.