scholarly journals INTERACTIONS OF WAVES WITH SUBMARINE TRENCHES

1980 ◽  
Vol 1 (17) ◽  
pp. 49
Author(s):  
Jiin-Jen Lee ◽  
Robert M. Ayer ◽  
Wen-Li Chiang
Keyword(s):  
Infinite Number ◽  
Water Waves ◽  
Laboratory Experiments ◽  
Normal Derivative ◽  
Two Dimensional ◽  
Final Solution ◽  
Reflection And Transmission ◽  
Common Boundary ◽  
Flow Configuration ◽  
Transmission Coefficients

An analysis is presented for the propagation of water waves past a submarine trench of irregular shape. Two dimensional, linearized potential flow is assumed. The fluid domain is divided into two regions along the mouth of the trench. Solutions in each region are expressed in terms of the unknown normal derivative of the potential function along this common boundary with the final solution obtained by matching. Reflection and transmission coefficients are found for various submarine geometries. The accuracy of the technique employed is demonstrated by comparing with previously published results for a rectangular trench. In addition, results from limited laboratory experiments were included for comparison. The result shows that for a particular flow configuration, there exists an infinite number of discrete wave frequencies at which waves are completely transmitted.

Wave propagation over a rectangular trench

1981 ◽  
Vol 110 ◽  
pp. 335-347 ◽  
Author(s):  
Jiin-Jen Lee ◽  
Robert M. Ayer
Keyword(s):  
Water Waves ◽  
Laboratory Experiments ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Final Solution ◽  
Reflection And Transmission ◽  
Common Boundary ◽  
Transmission Coefficients ◽  
Matching Procedure

An analysis is presented for the propagation of water waves past a rectangular submarine trench. Two-dimensional, linearized potential flow is assumed. The fluid domain is divided into two regions along the mouth of the trench. Solutions in each region are expressed in terms of the unknown normal derivative of the potential function along this common boundary with the final solution obtained by matching. Reflection and transmission coefficients are found for various submarine geometries. The result shows that, for a particular flow configuration, thereexists an infinite number of discrete wave frequencies at which waves are completely transmitted. The validity of the solution in the infinite constant-water-depth region is shown by comparing with the results using the boundary integral method for given velocity distributions along the mouth of the trench. The accuracy of the matching procedure is also demonstrated through the results of the boundary integral technique. In addition, laboratory experiments were performed and are compared with the theory for two of the cases considered.

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.

A NOTE ON DIFFRACTION BY AN INFINITE SLIT

1960 ◽  
Vol 38 (1) ◽  
pp. 38-47 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Integral Equation ◽  
Normal Derivative ◽  
Cylindrical Wave ◽  
Narrow Slit ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Boundary Values ◽  
Transmission Coefficients ◽  
Differential Integral Equation

The two-dimensional problem of diffraction of a plane wave by a narrow slit is considered. The assumed boundary values on the screen are the vanishing of either the total wave function or its normal derivative. In the former case, a differential–integral equation is obtained for the unknown function in the slit; in the latter, a pure integral equation is found. Solutions to these equations are given in the form of series in powers of ε (where ε/π is the ratio of slit width to wavelength), the coefficients of which depend on log ε. Expressions are found for the transmission coefficients as functions of ε and the angle of incidence; these are compared with previous determinations of other authors.A brief outline is given for the treatment of diffraction of a cylindrical wave by the slit.

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.

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.

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.

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.

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.

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