The scattering of surface waves by a vertical plane barrier

1969 ◽  
Vol 66 (2) ◽  
pp. 417-422 ◽  
Author(s):  
R. J. Jarvis ◽  
B. S. Taylor
Keyword(s):  
Surface Waves ◽  
Small Amplitude ◽  
Vertical Plane ◽  
Finite Depth ◽  
Infinite Depth ◽  
Plane Barrier

AbstractIn this paper we use a method due to Williams(1) to discuss the scattering of surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending indefinitely downwards from a finite depth.

A porous-wavemaker theory

1983 ◽  
Vol 132 ◽  
pp. 395-406 ◽  
Author(s):  
Allen T. Chwang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Small Amplitude ◽  
Vertical Plate ◽  
Hydrodynamic Pressure ◽  
Finite Depth ◽  
Wave Profile ◽  
Total Force ◽  
Wave Effect ◽  
Effect Parameter

A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail.

The radiation and scattering of surface waves by vertical barriers

1974 ◽  
Vol 63 (4) ◽  
pp. 625-634 ◽  
Author(s):  
D. Porter
Keyword(s):  
Boundary Value Problem ◽  
Surface Waves ◽  
Incident Wave ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Vertical Plane ◽  
Wave Radiation ◽  
Two Dimensional ◽  
Radiation Problem ◽  
Vertical Barriers

A train of small-amplitude surface waves is incident normally on an arbitrary arrangement of thin barriers lying in a vertical plane in deep water. Each barrier is allowed to make small rolling or swaying oscillations of the same frequency as that of the incident wave. The boundary-value problem for the consequent fluid motion, assumed two-dimensional, is solved exactly using a technique which enables the amplitudes of the scattered waves far from the barriers to be readily determined. Reference is made to the associated wave radiation problem and to the calculation of forces and moments on the barriers.

An explicit Hamiltonian formulation of surface waves in water of finite depth

1992 ◽  
Vol 237 ◽  
pp. 435-455 ◽  
Author(s):  
A. C. Radder
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Hamiltonian Formulation ◽  
Vertical Plane ◽  
Finite Depth ◽  
Short Wave ◽  
Linear Dispersion ◽  
Energy Functionals ◽  
Canonical Variables ◽  
Wave Nonlinearity

A variational formulation of water waves is developed, based on the Hamiltonian theory of surface waves. An exact and unified description of the two-dimensional problem in the vertical plane is obtained in the form of a Hamiltonian functional, expressed in terms of surface quantities as canonical variables. The stability of the corresponding canonical equations can be ensured by using positive definite approximate energy functionals. While preserving full linear dispersion, the method distinguishes between short-wave nonlinearity, allowing the description of Stokes waves in deep water, and long-wave nonlinearity, applying to long waves in shallow water. Both types of nonlinearity are found necessary to describe accurately large-amplitude solitary waves.

scholarly journals Small amplitude capillary-gravity waves in a channel of finite depth

1989 ◽  
Vol 31 (2) ◽  
pp. 142-160 ◽  
Author(s):  
M. C. W. Jones
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Gravity Waves ◽  
Small Amplitude ◽  
Unsolved Problem ◽  
Equations Of Motion ◽  
Finite Depth ◽  
Wave Problem ◽  
Infinite Depth ◽  
Existence And Multiplicity

Introductory Remarks. Recently a number of studies (Chen & Saffman [2], Jones & Toland [7,11], Hogan [5]) have been made of periodic capillary-gravity waves which form the free surface of an ideal fluid contained in a channel of infinite depth. However, little work appears to have been done on the corresponding problem when the depth is finite. The most significant contributions appear to be those of Reeder & Shinbrot [9], Barakat & Houston [1] and Nayfeh [8] all of whom confined themselves to Wilton ripples (see §1.3). Yet there are sound reasons why such a study should be made. For quite apart from the unsolved problem regarding the type of capillary-gravity waves which may occur at finite depths, the consideration of the finite depth problem may be regarded as a first step in the study of solitary capillary-gravity waves. In this paper, a new integral equation for the infinite depth problem, due to J. F. Toland and the author, is adapted to be of use in tackling the finite depth problem. Using this we obtain results for the exact equations of motion which answer rigorously the questions of existence and multiplicity of small amplitude solutions of the periodic capillary-gravity wave problem of finite depth.

Water Waves Over a Channel of Finite Depth With a Submerged Plane Barrier

1950 ◽  
Vol 2 ◽  
pp. 210-222 ◽  
Author(s):  
Albert E. Heins
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Finite Depth ◽  
The Third ◽  
Plane Barrier

This is the third in a series of problems in the study of surface waves which have been disturbed by the presence of a plane barrier and to which a solution may be provided. We assume as in part I, that the fluid is incompressible and non-viscous, and that motion is irrotational.

scholarly journals scattering of surface waves by a half immersed circular cylinder in fluid of finite depth

1985 ◽  
Vol 8 (1) ◽  
pp. 113-125
Author(s):  
Birendranath Mandel ◽  
Sudip Kumar Goswami
Keyword(s):  
Integral Equation ◽  
Circular Cylinder ◽  
Surface Waves ◽  
Velocity Potential ◽  
Finite Depth ◽  
Reflection Coefficients ◽  
Infinite Depth ◽  
Transmission And Reflection Coefficients ◽  
Linearized Theory ◽  
Transmission And Reflection

A train of surface waves is normally incident on a half immersed circular cylinder in a fluid of finite depth. Assuming the linearized theory of fluid under gravity an integral equation for the scattered velocity potential on the half immersed surface of the cylinder is obtained. It has not been found possible to solve this in closed form even for infinite depth of fluid. Our purpose is to obtain the asymptotic effect of finite depth “h” on the transmission and reflection coefficients when the depth is large. It is shown that the corrections to be added to the infinite depth results of these coefficients can be expressed as algebraic series in powers ofa/hstarting with(a/h)2where “a” is the radius of the circular cylinder. It is also shown that the coefficients of(a/h)2in these corrections do not vanish identically.

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

1971 ◽  
Vol 70 (2) ◽  
pp. 323-337 ◽  
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.

The diffraction of an obliquely incident surface wave by a vertical barrier of finite depth

1966 ◽  
Vol 62 (4) ◽  
pp. 829-838 ◽  
Author(s):  
T. R. Faulkner
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Deep Sea ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Finite Depth ◽  
Two Dimensional ◽  
Obliquely Incident ◽  
Vertical Barrier

The effect of a vertical barrier, fixed in an infinitely deep sea, on normally incident surface waves of small amplitude was first considered by Ursell (1) and generalizations which retain the two-dimensional aspects of the problem have subsequently been considered by John (2) and Lewin (3). The fluid motion due to the flexural vibrations of a barrier of finite depth has been considered by Alblas (4), the motion in this case being three-dimensional.

On the short surface waves due to a half-immersed circular cylinder oscillating on water of infinite depth

1982 ◽  
Vol 384 (1787) ◽  
pp. 333-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Surface Waves ◽  
Usual Method ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Small Kernel ◽  
Rolling Mode ◽  
Incident Waves ◽  
Plausible Argument ◽  
Fixed Cylinder

In this paper we examine two-dimensional short surface waves in water of infinite depth produced by various modes of oscillation of a half-immersed circular cylinder. The usual method, which depends on finding the potential on the cylinder from an integral equation with a small kernel, is here replaced by one that uses instead the known value of the potential for incident waves in the presence of the fixed cylinder. Thus we are able to determine three-term asymptotic expansions for both the heaving and the swaying modes that improve on earlier forms, and, for the heaving mode, to refine the interpolation with previous numerical calculations and confirm in principle the result obtained elsewhere by a plausible argument. The rolling mode also can actually be included by superposition of the heaving and swaying modes for this cylinder.

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