OBLIQUE WAVE SCATTERING BY A RECTANGULAR SUBMARINE TRENCH

2015 ◽  
Vol 56 (3) ◽  
pp. 286-298 ◽  
Author(s):  
RUMPA CHAKRABORTY ◽  
B. N. MANDAL
Keyword(s):  
Water Waves ◽  
Wave Scattering ◽  
Wave Train ◽  
Galerkin Approximation ◽  
Central Line ◽  
Wave Number ◽  
Reflection And Transmission ◽  
Oblique Wave ◽  
Transmission Coefficients ◽  
Linearized Theory

The problem of oblique wave scattering by a rectangular submarine trench is investigated assuming a linearized theory of water waves. Due to the geometrical symmetry of the rectangular trench about the central line $x=0$, the boundary value problem is split into two separate problems involving the symmetric and antisymmetric potential functions. A multi-term Galerkin approximation involving ultra-spherical Gegenbauer polynomials is employed to solve the first-kind integral equations arising in the mathematical analysis of the problem. The reflection and transmission coefficients are computed numerically for various values of different parameters and different angles of incidence of the wave train. The coefficients are depicted graphically against the wave number for different situations. Some curves for these coefficients available in the literature and obtained by different methods are recovered.

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.

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.

Propagation of Gravity Waves Past Multiple Bottom-Standing Barriers

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
D. Karmakar ◽  
C. Guedes Soares
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Wave Interaction ◽  
Offshore Structures ◽  
Least Square ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Edge Conditions ◽  
Linearized Theory ◽  
Flexible Barriers

The interaction of oblique surface gravity waves with multiple bottom-standing flexible porous breakwaters is analyzed based on the linearized theory of water waves. Using the method of eigenfunction expansion and the least square approximation, the wave propagation in the presence of single bottom-standing barriers is analyzed considering the upper edge to be: (i) free and (ii) moored, whereas the lower edge is considered to be clamped at the bottom. The wide-spacing approximation is used to analyze the wave interaction with multiple porous bottom-standing flexible barriers to understand the effect of the submerged flexible barriers as an effective breakwater. A brief comparison of both the upper edge conditions is carried out to analyze the effect of wave dissipation due to the presence of multiple barriers. The numerical results for the reflection and transmission coefficients along with the free surface vertical deflection are obtained for the case of two and three multiple bottom-standing barriers. The attenuation in the wave height due to the presence of porosity, change in barrier depth, and distance between the barriers are analyzed. The present study will be helpful in the analysis of proper functioning of porous bottom-standing barrier as an effective breakwater for the protection of offshore structures.

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.

Reflection and Transmission Coefficients for Two- and Three-Dimensional Quantum Wires

1997 ◽  
Vol 11 (23) ◽  
pp. 2777-2790 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Reflection Coefficient ◽  
Quantum Wires ◽  
Three Dimensional ◽  
Variable Cross Section ◽  
Wave Number ◽  
Variable Cross ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Matrix Differential Equations ◽  
Matrix Differential

The problem of a quantum wire connected smoothly on both sides to leads of variable cross section is studied. A method for solving this problem in terms of a set of nonlinear first order matrix differential equations for the variable reflection amplitude is discussed. The reflection coefficient obtained in this way is directly related to the conductivity, and is calculated as a function of the energy of the ballistic electrons. This formulation can be applied to three-dimensional as well as two dimensional quantum wires. For two specific cases the reflection coefficient is obtained as a function of the wave number of the incident electron, and the contribution of quantum tunneling to the transmission in each case is demonstrated. Also a model with a dissipative force is introduced and its effect on the transmission of the electrons is investigated.

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.

On the scattering of short surface waves by a finite dock

1968 ◽  
Vol 64 (4) ◽  
pp. 1109-1129 ◽  
Author(s):  
F. G. Leppington
Keyword(s):  
Wave Train ◽  
Normal Incidence ◽  
Great Depth ◽  
Travelling Wave ◽  
Reflection And Transmission ◽  
Large Wave ◽  
Transmission Coefficients ◽  
Weakly Coupled ◽  
Wave Trains ◽  
Induced Velocity

AbstractA sinusoidal travelling wave-train is at normal incidence upon a two-dimensional finite dock fixed on the surface of a body of water of great depth, and the problem investigated herein is that of finding the limiting form of the induced velocity potential for short waves. Of particular interest are the amplitudes of the wave-trains reflected and transmitted towards infinity by such an obstacle. The potential is expressed as a sum of coupled semi-infinite dock potentials, whence results a pair of weakly coupled integral equations for the solution. This formulation of the problem is shown to be amenable to an approximate solution for large wave-numbers, and the first few terms are derived in formal expansions for the reflection and transmission coefficients.

scholarly journals Effect of Capillarity on Fourth Order Nonlinear Evolution Equation for Two Stokes Wave Trains in Deep Water in the Presence of Air Flowing Over Water

2015 ◽  
Vol 20 (2) ◽  
pp. 267-282
Author(s):  
A.K. Dhar ◽  
J. Mondal
Keyword(s):  
Fourth Order ◽  
Deep Water ◽  
Water Waves ◽  
Nonlinear Evolution ◽  
Wave Train ◽  
Nonlinear Evolution Equations ◽  
Wave Number ◽  
Stokes Wave ◽  
Instability Wave ◽  
Starting Point

Abstract Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves, are derived for deep water surface capillary gravity waves in the presence of second waves in which air is blowing over water. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. A stability analysis is made for a uniform wave train in the presence of a second wave train. Graphs are plotted for the maximum growth rate of instability wave number at marginal stability and wave number separation of fastest growing sideband component against wave steepness. Significant improvements are noticed from the results obtained from the two coupled third order nonlinear Schrödinger equations.

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.

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