The interaction of waves with a row of circular cylinders

1993 ◽  
Vol 251 ◽  
pp. 687-708 ◽  
Author(s):  
C. M. Linton ◽  
D. V. Evans
Keyword(s):  
Water Waves ◽  
Circular Cylinders ◽  
Far Field ◽  
Incident Plane Wave ◽  
Straightforward Manner ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Incident Plane ◽  
Multipole Expansions ◽  
Field Behaviour

The two-dimensional acoustics problem of the scattering of an obliquely incident plane wave by a row of equally-spaced circular cylinders is solved using multipole expansions. The method is superior to existing techniques available for this problem as it allows the far-field behaviour of the solution to be evaluated in a straightforward manner, and extensive results for the reflection and transmission coefficients are given. The problem described above has a direct analogue in the theory of water waves and this is also discussed.

Characteristics of Bragg Reflection of Water Waves by Multiple Vertical Flexible Membranes

2018 ◽  
Author(s):  
Wei-Wei Ding ◽  
Zao-Jian Zou ◽  
Jing-Ping Wu
Keyword(s):  
Water Waves ◽  
Bragg Reflection ◽  
Least Square ◽  
Reflection And Transmission Coefficients ◽  
Effective Bandwidth ◽  
Linear Wave ◽  
Reflection And Transmission ◽  
Flexible Membrane ◽  
Transmission Coefficients ◽  
Flexible Membranes

Bragg reflection of water waves by multiple vertical flexible membranes in water of uniform depth is investigated based on the assumption of linear wave theory and small membrane deflection. The multiple vertical flexible membranes consist of several floating vertical flexible membranes which are installed with both ends fixed. First, a single vertical flexible membrane in water waves is considered, and the reflection and transmission coefficients are obtained based on the eigenfunction expansion method and the least square method. Then the interaction of water waves with the multiple vertical flexible membranes is studied. Using the reflection and transmission coefficients obtained for the single flexible membrane, the reflection and transmission coefficients of the multiple vertical flexible membranes are obtained based on the wide spacing approximation. The proposed method is proved to be efficient by comparing the calculated coefficients with the results published in literature. The characteristics of Bragg reflection, such as the occurring condition, the primary amplitude and the effective bandwidth, are systematically investigated under various factors including the number, the tension, the draft and the spacing of membranes. The results of the present study have certain reference value for design of multiple vertical flexible membranes as effective floating breakwaters.

Interaction of waves with two-dimensional obstacles: a relation between the radiation and scattering problems

1975 ◽  
Vol 71 (2) ◽  
pp. 273-282 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Water Waves ◽  
The Body ◽  
Far Field ◽  
Linear Superposition ◽  
Scattering Problems ◽  
Simple Argument ◽  
Transmission Coefficients ◽  
Horizontal Symmetry ◽  
Phase Angles ◽  
Formal Application

A relation connecting the reflexion and transmission coefficients for scattering of water waves by a fixed body with the far-field radiated waves due to forced motions of the same body is derived. Two alternative derivations are given, including a simple argument based on the analysis of an appropriate linear superposition of the two problems, and a more formal application of Green's theorem to the two potentials. For bodies with horizontal symmetry, the transmission and reflexion coefficients are related to the phase angles of the far-field radiated waves associated with symmetric and antisymmetric forced motions of the body. Some general conclusions follow for arbitrary symmetric bodies, and these are verified in specific cases by comparison with existing solutions. The applicability of these relations to other types of wave problem is noted.

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

1984 ◽  
Vol 96 (2) ◽  
pp. 359-369 ◽  
Author(s):  
B. N. Mandal ◽  
S. K. Goswami
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Number ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Obliquely Incident ◽  
Surface Water Waves

AbstractThe problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.

On the scattering of water waves by a submerged slender barrier

1998 ◽  
Vol 40 (2) ◽  
pp. 171-189
Author(s):  
P. K. Kundu ◽  
N. K. Saha
Keyword(s):  
Finite Length ◽  
Water Waves ◽  
Vertical Plate ◽  
Perturbation Technique ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
First Order ◽  
Transmission Coefficients ◽  
Special Cases ◽  
Analytical Expressions

AbstractAn approximate analysis, based on the standard perturbation technique, is described in this paper to find the corrections, up to first order to the reflection and transmission coefficients for the scattering of water waves by a submerged slender barrier, of finite length, in deep water. Analytical expressions for these corrections for a submerged nearly vertical plate as well as for a submerged vertically symmetric slender barrier of finite length are also deduced, as special cases, and identified with the known results. It is verified, analytically, that there is no first order correction to the transmitted wave at any frequency for a submerged nearly vertical plate. Computations for the reflection and transmission coefficients up to O(ε), where ε is a small dimensionless quantity, are also performed and presented in the form of both graphs and tables.

scholarly journals WATER WAVE SCATTERING BY ROWS OF CIRCULAR CYLINDERS

1988 ◽  
Vol 1 (21) ◽  
pp. 164 ◽  
Author(s):  
Robert A. Dalrymple ◽  
Seung Nam Seo ◽  
Paul A. Martin
Keyword(s):  
Experimental Data ◽  
Finite Number ◽  
Water Wave ◽  
Wave Scattering ◽  
Reflection And Transmission Coefficients ◽  
Circular Cylinders ◽  
Reflection And Transmission ◽  
Water Wave Scattering ◽  
Single Row ◽  
Transmission Coefficients

The scattering of waves by a finite number of rows of circular cylinders is examined. Reflection and transmission coefficients are obtained and compared to Kakuno's experimental data. Following Twersky (1962), the scattering from a single row of cylinders (or the single grating problem) is numerically solved. The wide-spacing approximation is used to find the effect of multiple gratings.

The influence of surface tension on the reflection of water waves by a plane vertical barrier

1968 ◽  
Vol 64 (3) ◽  
pp. 795-810 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Related Problem ◽  
Velocity Potential ◽  
Surface Tension Force ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Reflected Wave ◽  
Vertical Barrier ◽  
Effect Of Surface

AbstractIn this paper the effect of surface tension is included in a well-known problem in the theory of two-dimensional infinitesimal water waves. The problem is that of the reflection of waves from a fixed vertical barrier immersed to a depth a into deep water. It is shown how the solution for the velocity potential may be determined uniquely when simple assumptions are made concerning the behaviour of the free surface near the barrier. In particular, expressions are derived for the reflection coefficient, defined as the ratio of the amplitude of the reflected wave to that of the incident wave, at infinity, and the transmission coefficient, defined similarly. It is shown how these coefficients, for small values of the surface tension force, tend to the values obtained by Ursell (4) when surface tension is ignored. The related problem of a completely immersed vertical barrier extending to a distance a from the surface may be solved in a similar manner. Expressions for the reflection and transmission coefficients for this case are given.

Reflection and transmission of surface waves at a vertical interface in anisotropic elastic media

1993 ◽  
Vol 83 (5) ◽  
pp. 1355-1372
Author(s):  
E. N. Its ◽  
J. S. Lee
Keyword(s):  
Surface Waves ◽  
Wave Reflection ◽  
Analytical Procedure ◽  
Far Field ◽  
Elastic Media ◽  
Reflection And Transmission ◽  
Trade Off ◽  
Transmission Coefficients ◽  
Dyadic Representation ◽  
Anisotropic Elastic

Abstract Propagation of surface waves across a vertical interface between anisotropic blocks is considered in this paper. Dyadic representation of a far field Green's function for an anisotropic half-space is constructed first. An analytical procedure is then developed to determine the reflection and transmission coefficients of surface waves at the vertical interface between two laterally homogeneous anisotropic quarter-spaces. Numerical results of Rayleigh wave reflection at vertical interfaces between dissimilar blocks are presented and the trade-off between anisotropy and inhomogeneity is discussed.

scholarly journals WATER-WAVES SCATTERING BY PERMEABLE BOTTOM IN TWO-LAYER FLUID IN THE PRESENCE OF SURFACE TENSION

2017 ◽  
Vol 22 (6) ◽  
pp. 827-851 ◽  
Author(s):  
Srikumar Panda ◽  
Subash C. Martha
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Reflection And Transmission Coefficients ◽  
Wave Number ◽  
Physical Parameters ◽  
Fluid System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linearized Theory ◽  
Incident Waves

In the present paper, reflection and transmission phenomena of water waves due to undulating permeable bottom in a two-layer fluid system are investigated using two-dimensional linearized theory. The effect of surface tension on the free surface is included in this work. In two-layer fluid system, there exist waves with two different wave numbers (modes). When a wave of a particular wave number encounters the undulating bottom, reflection and transmission phenomena occur in both the layers. The reflection and transmission coefficients in both layers due to incident waves of both modes are analyzed with the aid of perturbation analysis along with Fourier transform technique. It is found that these coefficients are obtained in terms of integrals which depend on the shape function of the undulating bottom. Two different kinds of undulating bottoms are considered to determine these coefficients. For a particular undulating bottom, namely sinusoidal bottom undulation the effect of various physical parameters such as number of ripples, surface tension and porous effect parameters are demonstrated graphically. The study further elaborates the energy balance relations associated with the reflection and transmission coefficients to ascertain the correctness of all the computed results.

Radiation and scattering of water waves by rigid bodies

1971 ◽  
Vol 46 (1) ◽  
pp. 151-164 ◽  
Author(s):  
J. L. Black ◽  
C. C. Mei ◽  
M. C. G. Bray
Keyword(s):  
Surface Waves ◽  
Incident Wave ◽  
Water Waves ◽  
Variational Formulation ◽  
Rigid Bodies ◽  
Small Oscillation ◽  
Circular Cylinders ◽  
Wave Forces ◽  
Far Field ◽  
Plane Incident Wave

Schwinger's variational formulation is applied to the radiation of surface waves due to small oscillation of bodies. By means of Haskind's theorem the wave forces on a stationary body due to a plane incident wave are found using only far-field properties. Results for horizontal rectangular and vertical circular cylinders are presented.

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