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Journal ArticleDOI

On the generation of water waves at an inertial surface

01 Jan 1984-The Journal of The Australian Mathematical Society. Series B. Applied Mathematics (Australian Mathematical Society)-Vol. 25, Iss: 3, pp 366-383
TL;DR: On developpe une methode de transformee de Laplace as mentioned in this paper for resoudre les problemes de valeur initiale, le potentiel de vitesse decrivant la generation d'ondes de gravite capillaires infinitesimales dans un liquide au repos avec une surface inertielle composee de particules flottantes distribuees uniformement.
Abstract: On developpe une methode de transformee de Laplace pour resoudre les problemes de valeur initiale, le potentiel de vitesse decrivant la generation d'ondes de gravite capillaires infinitesimales dans un liquide au repos avec une surface inertielle composee de particules flottantes distribuees uniformement

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Citations
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Journal ArticleDOI
TL;DR: In this article, a linear Cauchy-Poisson problem was solved for the first time when a shear current of uniform vorticity is present beneath the surface, including the effects of gravity, surface tension, and constant finite depth.
Abstract: We solve for the first time the classical linear Cauchy-Poisson problem—the time evolution of an initial surface disturbance—when a shear current of uniform vorticity is present beneath the surface. The solution is general, including the effects of gravity, surface tension, and constant finite depth. The particular case of an initially Gaussian disturbance of width b is studied for different values of three system parameters: a “shear Froude number” Sb/g (S is the vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well-known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are anal...

38 citations

Journal ArticleDOI
D.Q. Lu1, S.Q. Dai1
TL;DR: In this paper, wave motion due to line, point and ring sources submerged in an inviscid fluid is analyzed in the framework of potential flow, where the perturbed flow is decomposed into the regular and the singular components.

35 citations


Cites background from "On the generation of water waves at..."

  • ...In particular, as the flexural rigidity of the plate tends to zero, the plate-covered surface reduces to the inertial surface [5] which represents the effect of a thin uniform distribution of non-interacting floating matter, for example,...

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors solved the linear Cauchy-poisson problem for the time evolution of an initial surface disturbance when a uniform shear current is present beneath the surface.
Abstract: We solve for the first time the classical linear Cauchy--Poisson problem for the time evolution an initial surface disturbance when a uniform shear current is present beneath the surface. The solution is general, including the effects of gravity, surface tension and constant finite depth. The particular case of an initially Gaussian disturbance of width $b$ is studied for different values of three system parameters: a "shear Froude number" $S\sqrt{b/g}$ ($S$ is the uniform vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are analysed and explained in light of the shear-modified dispersion relation.

27 citations

Journal ArticleDOI
TL;DR: In this article, the Laplace transform technique is employed to obtain their solutions for initial value problems and Graphs of particular integrals appearing in the representations of the potential functions are presented, which confirm that the expressions thus derived are suitable for numerical computation for all possible combinations of the positions of the field point and the source point.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the Laplace transform technique is used to solve an initial value problem describing waves generated by a disturbance created at the surface of water covered by an inertial surface composed of a thin but uniform distribution of floating particles.
Abstract: Laplace transform technique is used to solve an initial value problem describing waves generated by a disturbance created at the surface of water covered by an inertial surface composed of a thin but uniform distribution of floating particles. Green's integral theorem produces the transformed potential function from which the form of the inertial surface is obtained as an infinite integral after taking Laplace inversion. The method of stationary phase is then employed to evaluate this integral approximately for large time and distance.

16 citations

References
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01 Jul 1958
TL;DR: In this paper, the evanescent field structure over the wave front, as represented by equiphase planes, is identified as one of the most important and easily recognizable forms of surface wave.
Abstract: This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

1,244 citations

Journal ArticleDOI
01 Oct 1953
TL;DR: In this article, the authors considered the problem of the generation of surface waves by a submerged circular cylinder and used a series of complex potential functions arising from multipoles at the centre of the cylinder, but the velocity potential of the motion could have been described, without the introduction of the stream function.
Abstract: Problems dealing with the generation of surface waves in water involve the consideration of singularities of different types in the liquid. In the case when bodies are present in the liquid, waves may be either generated by the movement of the body, or reflected from the body. The two cases are essentially equivalent, and the resulting motion can be described by a series of singularities placed within the body. The boundary conditions on the surface of the body give equations from which the exact form of the potential can be obtained. Ursell (10) has solved in this manner the problem, earlier discussed by Dean(1), of the generation of surface waves by a submerged circular cylinder. In this two-dimensional problem he used a series of complex potential functions arising from multipoles at the centre of the cylinder, but the velocity potential of the motion could have been described, without the introduction of the stream function, in terms of the velocity potentials of the multipoles.

176 citations