Singularities in a two-fluid medium
TL;DR: In this article, the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity, was computed for the case where the fluids are nonviscous and incompressible, the upper one of finite depth with a free surface.
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Abstract: We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered
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Citations
On wave motion in a two-layered liquid of infinite depth in the presence of surface and interfacial tension
TL;DR: In this paper, the wave-source potentials are used to construct the set of slope potentials that produce discontinuous free-surface and interface slopes, which are then utilized to obtain the potentials for waves due to both heaving vertical plates and incident progressive waves against a vertical wall.
Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz's equation
TL;DR: In this paper, velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodal along its length.
Wave scattering by a thin vertical barrier in a two-layer fluid
TL;DR: In this paper, the scattering of surface and interface waves by a vertical plate in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of density greater than the upper layer is studied.
5
Internal waves against a vertical cliff at the interface between two superposed fluids
TL;DR: In this article, a linear solution to the 3D problem of incoming internal waves at the surface separating two fluids against a vertical cliff is presented, and analytical expressions for velocity potentials in each of the fluids are obtained.
1
On the waves in two superposed liquids in the presence of a wall
Partha Agasti,Prabir Kumar Kundu +1 more
TL;DR: An exact analysis is described for finding the linear solution of the normally incident incoming waves in the presence of surface tension (ST) in two liquids, where the liquids are bounded on the left by a rigid vertical wall.
1
References
Multipole expansions in the theory of surface waves
R. C. Thorne,F. Ursell +1 more
- 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.
185
Fundamental singularities in the theory of water waves with surface tension
TL;DR: In this paper, the authors obtained the forms for the harmonic potential functions describing the fundamental wave-source and multipole singularities which pertain to the study of infinitesimal time-harmonic waves on the free surface of water when the effect of surface tension is included.
33
Basic singularities in the theory of internal waves
M. A. Gorgui,S. E. Kassem +1 more
TL;DR: In this article, a complete survey of the line and point singularities for the case of finite constant thickness is presented, where the surface tension at the surface of separation is not considered.
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