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    Wyświetlanie 1-6 z 6
    Tytuł:
    Oblique water wave diffraction by a step
    Autorzy:
    Dolai, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/264885.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    finite step
    Havelock expansion
    Galerkin approximation
    Gegenbauer polynomial
    reflection and transmission coefficients
    aproksymacja Galerkina
    wielomian Gegenbauera
    odbicie
    Opis:
    This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for reflection and transmission coefficients which are depicted graphically. From these figures various interesting results are discussed.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2017, 22, 1; 35-47
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Scattering of interface wave by bottom undulations in the presence of thin submerged vertical wall with a gap
    Autorzy:
    Dolai, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/265016.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dyfrakcja fal
    fala powierzchniowa
    fala grawitacyjna
    submerged vertical wall
    perturbation analysis
    interface wave scattering
    sinusoidal bottom
    Galerkin approximations
    zero-order reflection coefficient
    first-order reflection coefficient
    Opis:
    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.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2016, 21, 2; 303-322
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Scattering of internal waves by vertical barrier in a channel of stratified fluid
    Autorzy:
    Dolai, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/264794.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    stratified fluid
    internal wave
    vertical barrier
    stream function
    scattering matrix
    Boussinesq approximation
    eigen function expansion
    rozwarstwienie
    hydromechanika
    fala wewnętrzna
    Opis:
    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.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2015, 20, 3; 471-485
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Scattering of oblique water waves by an infinite step
    Autorzy:
    Dolai, P.
    Dolai, D. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/265749.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    aproksymacja Galerkina
    wielomian Gegenbauera
    współczynnik transmisji
    infinite step
    Havelock expansion
    Galerkin approximation
    Gegenbauer polynomial
    reflection and transmission coefficients
    Opis:
    The present paper is concerned with the problem of scattering of obliquely incident surface water wave train passing over a step bottom between the regions of finite and infinite depth. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain very accurate numerical estimates for reflection and transmission coefficients. The numerical results are illustrated in tables.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2018, 23, 2; 327-338
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Internal wave diffraction by a strip of an elastic plate on the surface of a stratified fluid
    Autorzy:
    Dolai, P.
    Dolai, D. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/265771.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Kleina-Gordona
    płyn warstwowy
    metoda Wienera-Hopfa
    stratified fluid
    Klein-Gordon equation
    Wiener-Hopf technique
    steepest descent method
    Opis:
    The problem of internal wave diffraction by a strip of an elastic plate of finite width present on the surface of an exponentially stratified liquid is investigated in this paper. Assuming linear theory, the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves a hyperbolic type partial differential equation (PDE), known as the Klein Gordon equation. The method of Wiener-Hopf is utilized in the mathematical analysis to a slightly generalized boundary value problem (BVP) by introducing a small parameter, and the problem is solved approximately for large width of the plate. In the final results, this small parameter is made to tend to zero. The diffracted field is obtained in terms of integrals, which are then evaluated asymptotically in different regions for a large distance from the edges of the plate and the results are interpreted physically.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2013, 18, 1; 5-26
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Edge waves over a shelf
    Autorzy:
    Dolai, P.
    Dolai, D. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/264611.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fala brzegowa
    wielomian Gegenbauera
    relacja dyspersji
    shelf
    edge wave
    Havelock expansion
    Galerkin approximation
    Gegenbauer polynomial
    dispersion relation
    Opis:
    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.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2019, 24, 2; 453-460
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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