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 Solution of the problem of scattering of water waves by a nearly vertical plate

1994 ◽  
Vol 35 (3) ◽  
pp. 382-395 ◽  
Author(s):  
L. Vijaya Bharathi ◽  
A. Chakrabarti ◽  
B. N. Mandal ◽  
S. Banerjee
Keyword(s):  
Water Waves ◽  
Vertical Plate ◽  
Mixed Boundary ◽  
Complete Solution ◽  
Perturbation Techniques ◽  
Order Accuracy ◽  
Reflection And Transmission ◽  
First Order ◽  
Transmission Coefficients ◽  
Special Assumption

AbstractAn approximate solution is determined for the problem of scattering of water waves by a nearly vertical plate, by reducing it to two mixed boundary-value problems (BVP) for Laplace's equation, using perturbation techniques. While the solution of one of these BVP is well-known, the other BVPs is reduced to the problem of solving two uncoupled problems, and the complete solution of the problem under consideration up to first-order accuracy is derived with a special assumption on the shape of the plate and a related approximation. Known results involving the reflection and transmission coefficients are reproduced.

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.

Dilatational waves at a microstretch solid/fluid interface

2016 ◽  
Vol 23 (20) ◽  
pp. 3448-3467 ◽  
Author(s):  
Dilbag Singh ◽  
Neela Rani ◽  
Sushil Kumar Tomar
Keyword(s):  
Half Space ◽  
Aluminum Matrix ◽  
Elastic Solid ◽  
Specific Model ◽  
Reflection And Transmission Coefficients ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Special Cases ◽  
Microstretch Fluid

The present work is concerned with the study of reflection and transmission phenomena of dilatational waves at a plane interface between a microstretch elastic solid half-space and a microstretch liquid half-space. Eringen's theory of micro-continuum materials has been employed for addressing the mathematical analysis. Reflection and transmission coefficients, corresponding to various reflected and transmitted waves, have been obtained when a plane dilatational wave strikes obliquely at the interface after propagating through the solid half-space. It is found that the reflection and transmission coefficients are functions of the angle of incidence, the frequency of the incident wave and the elastic properties of the half-spaces. Numerical calculations have been carried out for a specific model by taking an aluminum matrix with randomly distributed epoxy spheres as the microstretch solid medium, while the microstretch fluid is taken arbitrarily with suitably chosen elastic parameters. The computed results obtained have been depicted graphically. The results of earlier studies have been deduced from the present formulation as special cases.

scholarly journals Modelling Reflection and Transmission of Acoustic Waves at a Semiconductor: Fluid Interface

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
A. Sharma ◽  
J. N. Sharma ◽  
Y. D. Sharma
Keyword(s):  
Acoustic Waves ◽  
Grazing Incidence ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Saw Devices ◽  
Special Cases ◽  
Gauss Elimination ◽  
Programming Software ◽  
Matlab Programming

The paper concentrates on the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor half-space underlying an inviscid liquid. The reflection and transmission coefficients varying with the incident angles are examined. Calculated results are verified by considering the quasilongitudinal () and quasitransverse () waves. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection and transmission coefficients are carried out with the help of Gauss elimination method by using MATLAB programming software for silicon (Si) and germanium (Ge) semiconductors. The computer simulated-results have been plotted graphically for Si and presented in tabular form in case of Ge semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

The viscoelastic reflection/transmission problem: Two special cases

1983 ◽  
Vol 73 (6A) ◽  
pp. 1673-1683
Author(s):  
E. S. Krebes
Keyword(s):  
Incident Wave ◽  
Incidence Angle ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
First Case ◽  
Special Cases ◽  
Mathematical Formulas ◽  
Linear Viscoelastic ◽  
Ray Bending

Abstract In the general problem of plane wave reflection and transmission at a boundary separating two linear viscoelastic media, the mathematical formulas for the reflection and transmission coefficients, the transmission angle, the attenuation vector, etc., are not easily interpretable because they cannot easily be expressed in terms of the basic input parameters (Q, incidence angle, etc.). To gain further insight, we study two special cases in which mathematical simplifications occur. No low-loss approximations are involved. In the first case, the incident wave is homogeneous, and the Q values of the two layers are equal, and we find, among other things, that the reflection and transmission coefficients are the same as the ones for perfect elasticity (they do not involve complex velocities, etc., and are independent of Q). In the second special case, the degree of inhomogeneity of the incident wave approaches its upper limit, and we find that the reflection and transmission coefficients approach constant (complex) values independent of the incidence angle, and that there is almost no ray-bending (refraction) upon transmission of the incident wave through the boundary.

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.

16.—Waves over Obstacles on a Shallow Seabed

1973 ◽  
Vol 71 (3) ◽  
pp. 181-192 ◽  
Author(s):  
Alan Jeffrey ◽  
Saw Tin
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Recurrence Relations ◽  
Reflection And Transmission Coefficients ◽  
Shallow Water Waves ◽  
Reflection And Transmission ◽  
Transmission Coefficients

SynopsisIn this paper we consider the effect of the passage of shallow water waves over vertical walled objects on a flat seabed. The effect of reflections at the successive walls is taken into account when determining the place of breaking of the wave. The results are obtained by the introduction of special reflection and transmission coefficients at each wall and recurrence relations are formulated connecting their values at successive walls. The effect of this is to reduce the calculation of the place of breaking of the wave over a stepped seabed to an equivalent one for a wave over a flat seabed, the result of which is well known.

scholarly journals Scattering of Oblique Water Waves by an Infinite Step

2018 ◽  
Vol 23 (2) ◽  
pp. 327-338
Author(s):  
P. Dolai ◽  
D.P. Dolai
Keyword(s):  
Surface Water ◽  
Water Waves ◽  
Water Wave ◽  
Wave Train ◽  
Reflection And Transmission Coefficients ◽  
Physical Parameters ◽  
Reflection And Transmission ◽  
Infinite Depth ◽  
Transmission Coefficients ◽  
Galerkin Approximations

AbstractThe present paper is concerned with the problem of scattering of obliquely incident surface water wave train passing over a step bottom between the regions of finite and infinite depth. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain very accurate numerical estimates for reflection and transmission coefficients. The numerical results are illustrated in tables.

scholarly journals Wave Scattering by Small Undulation on the Porous Bottom of an Ocean in the Presence of Surface Tension

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Srikumar Panda ◽  
Sudhanshu Shekhar Samantaray ◽  
S. C. Martha
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Bottom Topography ◽  
Wave Theory ◽  
Reflection And Transmission ◽  
First Order ◽  
Transmission Coefficients ◽  
Bottom Undulation ◽  
Surface Water Waves ◽  
The Fourier Transform

The scattering of incident surface water waves due to small bottom undulation on the porous bed of a laterally unbounded ocean in the presence of surface tension at the free surface is investigated within the framework of two-dimensional linearized water wave theory. Perturbation analysis in conjunction with the Fourier transform technique is employed to derive the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. One special type of bottom topography is considered as an example and the related coefficients are determined in detail. These coefficients are presented in graphical forms. The theoretical observations are validated computationally. The results for the problem involving scattering of water waves by bottom deformations on an impermeable ocean bed are obtained as a particular case.

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