Breaking probabilities for dominant surface waves on water of finite constant depth

A half-immersed circular cylinder of radius a undergoes a periodic heaving motion on water of finite constant depth h . The behaviour of the virtual mass is considered in the long-wave region where existing computations are in disagreement. For finite depth Ursell has recently confirmed analytically that the virtual mass remains finite (and is thus a function of a/h ) in the limit Ka = Kh = 0, a/h fixed. His long-wave investigation is now extended by a study of the gradient /d( virtual mass)/d(Aa) for small Ka . It is shown that this gradient is positive in the limit of zero frequency when a/h is sufficiently small, and that in this case the virtual mass has a maximum near Kh = 1. An argument is also given which suggests that this maximum may be expected for bodies of more general sections.

Download Full-text

Basic singularities in the theory of internal waves with surface tension

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171286000182 ◽

1986 ◽

Vol 9 (1) ◽

pp. 145-159

Author(s):

M. A. Gorgui ◽

M. S. Faltas

Keyword(s):

Surface Tension ◽

Internal Waves ◽

Constant Depth ◽

Two Fluids ◽

Interface Wave ◽

Different Types ◽

Superposed Fluids ◽

Wave Problems ◽

Effect Of Surface ◽

Finite Constant

The study of linearized interface wave problems for two superposed fluids often involves the consideration of different types of singularities in one of the two fluids. In this paper the line and point singularities are investigated for the case when each fluid is of finite constant depth. The effect of surface tension at the surface of separation is included.

Download Full-text

Multipole expansions for two superposed fluids, each of finite depth

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410005934x ◽

1982 ◽

Vol 91 (2) ◽

pp. 323-329 ◽

Cited By ~ 11

Author(s):

S. E. Kassem

Keyword(s):

Surface Tension ◽

Internal Waves ◽

Finite Depth ◽

Constant Depth ◽

Two Fluids ◽

Different Types ◽

Multipole Expansions ◽

Superposed Fluids ◽

Finite Constant

AbstractProblems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line and point multipoles are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.

Download Full-text

On the forced surface waves due to a vertical wave-maker in the presence of surface tension

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100049926 ◽

1971 ◽

Vol 70 (2) ◽

pp. 323-337 ◽

Cited By ~ 38

Author(s):

P. F. Rhodes-Robinson

Keyword(s):

Surface Tension ◽

Surface Waves ◽

Wave Motion ◽

Velocity Potential ◽

Vertical Plane ◽

Finite Depth ◽

Cylindrical Wave ◽

Constant Depth ◽

Classical Wave ◽

Wave Maker

AbstractThe classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.

Download Full-text

A note on the singularities in the theory of water waves with an inertial surface

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000005361 ◽

1986 ◽

Vol 28 (2) ◽

pp. 271-278 ◽

Cited By ~ 11

Author(s):

B. N. Mandal ◽

Krishna Kundu

Keyword(s):

Gravity Waves ◽

Water Waves ◽

Point Sources ◽

Time Dependent ◽

Constant Depth ◽

Inertial Surface ◽

Floating Particles ◽

Fundamental Line ◽

Finite Constant

AbstractThis note is concerned with the derivation of velocity potentials describing the generation of infinitesimal gravity waves in a motionless liquid with an inertial surface composed of uniformly distributed floating particles, due to fundamental line and point sources with time-dependent strengths submerged in a liquid of finite constant depth.

Download Full-text

Wave source potentials for two superposed fluids, each of finite depth

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100066329 ◽

1986 ◽

Vol 100 (3) ◽

pp. 595-599 ◽

Cited By ~ 9

Author(s):

S. E. Kassem

Keyword(s):

Surface Tension ◽

Internal Waves ◽

Finite Depth ◽

Constant Depth ◽

Wave Source ◽

Two Fluids ◽

Different Types ◽

Superposed Fluids ◽

Finite Constant

AbstractProblems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line sources are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.

Download Full-text