Forced gravity waves in two-layered fluids with the upper fluid having a free surface

2003 ◽  
Vol 81 (4) ◽  
pp. 675-689 ◽  
Author(s):  
H H Sherief ◽  
M S Faltas ◽  
E I Saad
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Harmonic Wave ◽  
Density Ratio ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids ◽  
Lower Fluid ◽  
Wave Maker

The steady-gravity wave motion is considered for two immiscible layers of incompressible and nonviscous fluids in the presence of a porous wave maker immersed vertically in the two fluids, the upper fluid having a free surface and the lower fluid is of infinite depth. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the wave maker. Also the scattering of a harmonic wave incident normally to the wave maker is considered and the reflection and transmission coefficients are obtained. The case when the lower fluid is of finite depth is also considered. The results are plotted for different values of porosity and different values of the density ratio. PACS Nos.: 47.35.+i, 47.55.Hd, 47.55.Mh

scholarly journals Reflection of internal waves by sand ripples

1995 ◽  
Vol 18 (1) ◽  
pp. 171-177
Author(s):  
Samiran Mandal ◽  
Uma Basu
Keyword(s):  
Integral Transform ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Interface Waves ◽  
Sand Ripples ◽  
Transmission Coefficients ◽  
Bottom Deformation ◽  
Time Harmonic ◽  
Lower Fluid ◽  
Superposed Fluids

An investigation is made to study the diffraction of a train of time harmonic progressive waves propagating along the surface of separation of two superposed fluids which are laterally unbounded, the upper fluid being extended infinitely upwards, the lower fluid being of finite depth with sand ripples at the bottom. The first order correction to the velocity potential for the problem of diffraction of interface waves in the presence of bottom deformation is obtained by integral transform technique after introduction of a linear frictional term in the kinematic boundary condition at the surface of separation following Lamb (1932), and the reflection and transmission coefficients are estimated for a patch of sand ripples.

The acoustic signature for a surface-breaking crack produced by a point focus microscope

1992 ◽  
Vol 438 (1902) ◽  
pp. 47-65 ◽  
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Acoustic Microscope ◽  
Transmission Coefficients ◽  
Acoustic Signature ◽  
Surface Breaking Crack ◽  
Line Focus ◽  
Fourier Integrals

The acoustic signature of a crack, breaking the surface of an otherwise homogeneous, isotropic elastic material, produced by a point focus scanning acoustic microscope is constructed theoretically. This work is patterned after a similar calculation carried out for the line focus microscope. The incident axisymmetric focused beam is constructed as a Fourier integral that produces a specified profile in the focal plane. The wavefields scattered from the specimen are also represented as Fourier integrals. Because the lens of the acoustic microscope is characterized by a large Fresnel number and an F number of order one, the Fourier integrals can be asymptotically approximated to obtain explicit expressions for the incident wavefield and for the wavefield scattered from a defect-free surface. The latter wavefield contains the leaky Rayleigh wave that is incident to the surface-breaking crack. The surface­-breaking crack is characterized by assigning it reflection and transmission coefficients. The wavefield scattered from the crack is estimated by tracing the leaky Rayleigh rays reflected and transmitted by the crack. The net wavefield scattered from the surface is then constructed by adding this crack scattered wavefield to that calculated for a defect-free surface. Lastly, the acoustic signature is calculated by using the appropriate incident and scattered wavefields in an electromechanical reciprocity identity that links the voltage measured at the microscope’s transducer to the scattered acoustic wavefields at the surface of the specimen. Expressions for acoustic signatures made using the line focus and point focus microscopes are compared. Moreover, from the expression for the acoustic signature, the Rayleigh wave reflection and transmission coefficients can be partly extracted.

Article

1998 ◽  
Vol 76 (7) ◽  
pp. 539-557
Author(s):  
M Burgess ◽  
M Carrington ◽  
G Kunstatter
Keyword(s):  
Initial Value Problem ◽  
Wave Motion ◽  
Generalized Functions ◽  
Incompressible Fluids ◽  
Horizontal Direction ◽  
Wave Number ◽  
Initial Value ◽  
Two Fluids ◽  
Wave Maker

The initial value problem of wave motion is considered for two immiscible layersof incompressible fluids in the presence of a porous wave maker immersed vertically in thetwo uids, which are periodic in the horizontal direction along the wave maker as well as intime. The resulting motion is investigated using the method of generalized functions, and anasymptotic analysis for large values of time and distance is given for the depression of thefree surface and the surface of separation between the two fluids. The generated fluid patternis discussed for different values of the wave number of the oscillations of the wave makervelocity in the horizontal direction. PACS No.: 47.35

scholarly journals Singularities in a two-fluid medium

1983 ◽  
Vol 6 (4) ◽  
pp. 737-754 ◽  
Author(s):  
Rathindra Nath Chakrabarti ◽  
Birendranath Mandal
Keyword(s):  
Horizontal Plane ◽  
Plane Surface ◽  
Finite Depth ◽  
Point Singularity ◽  
Fluid Medium ◽  
Two Fluids ◽  
Line Singularity ◽  
Lower Fluid ◽  
Irrotational Motion ◽  
Two Fluid

We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered.

Reflections, rays, and reverberations

1974 ◽  
Vol 64 (6) ◽  
pp. 1685-1696 ◽  
Author(s):  
B. L. N. Kennett
Keyword(s):  
Free Surface ◽  
Single Layer ◽  
Iterative Approach ◽  
Multilayered Media ◽  
Reflection And Transmission ◽  
Matrix Methods ◽  
Special Effects ◽  
Transmission Coefficients ◽  
Transmission Properties ◽  
Set Up

abstract The connection is established between conventional matrix methods for layered media and the reflection and transmission properties of a single layer. This interrelation is then used to set up an iterative approach to the calculation of reflection and transmission coefficients in multilayered media. This approach lends itself to a ray interpretation and allows estimates of errors involved in taking truncated partial ray expansions to be made. The special effects due to a free surface are also considered.

An Application of Elastodynamic Reciprocity to Reflection by an Obstacle in a Waveguide

2000 ◽  
Vol 16 (2) ◽  
pp. 97-101
Author(s):  
J.D. Achenbach
Keyword(s):  
Transverse Wave ◽  
Elastic Layer ◽  
Wave Motion ◽  
Elastic Solid ◽  
Orthogonality Condition ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Planar Array ◽  
Wave Modes

ABSTRACTThe reciprocal identity which connects two elastodynamic states, denoted by A and B, is used in this paper to obtain two results for an elastic layer. The first is an orthogonality condition for wave modes. For that case the states A and B are wave modes propagating in the same direction. The second result concerns reflection and transmission of wave motion by an obstacle in the layer. Now state A is defined by a superposition of incident wave modes and its reflection and transmission by the obstacle. Expressions for the reflection and transmission coefficients are obtained by selecting counter propagating wave modes for state B. It is also shown that the reflection by an obstacle in a layer can be extended to obtain the reflection and transmission coefficients for a planar array of obstacles in an unbounded elastic solid. For clarity all results are presented for horizontally polarized transverse wave motion.

Harmonic Wave Analysis of Vibration and Stress in a Longitudinally Reciprocated Bar

1970 ◽  
Vol 12 (3) ◽  
pp. 169-177 ◽  
Author(s):  
B. Beddoe
Keyword(s):  
Synthetic Fibre ◽  
Harmonic Wave ◽  
Unit Length ◽  
General System ◽  
Approximate Equation ◽  
Wave Dispersion ◽  
Steady State Solution ◽  
Longitudinal Motion ◽  
Reflection And Transmission ◽  
Transmission Coefficients

The wave equation in one dimension approximately represents the longitudinal motion of a uniform bar that carries regularly spaced equal point masses. Fourier analysis is used to obtain the steady-state solution when the bar is reciprocated from one end. Distributed damping is considered. The more general system of unequal and irregularly spaced point masses on a bar consisting of sections of different mass per unit length is analysed in terms of reflection and transmission coefficients; a wave reflection method and a transfer matrix method are given for the solution of the problem of reciprocation. The limitation of the approximate equation of motion is assessed by examining wave dispersion in the uniform system. Application to ‘traverse bars’ on machines for winding extruded synthetic fibre was the object of the investigation.

scholarly journals Scattering of water waves by rectangular thick barriers in presence of surface tension

2021 ◽  
Vol 23 (11) ◽  
pp. 30-55
Author(s):  
Gour Das ◽  
◽  
Rumpa Chakraborty ◽  
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Graphical Representation ◽  
Finite Depth ◽  
Approximation Technique ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Gegenbauer Polynomial ◽  
Incident Waves ◽  
Effect Of Surface

The influence of surface tension over an oblique incident waves in presence of thick rectangular barriers present in water of uniform finite depth is discussed here. Three different structures of a bottom-standing submerged barrier, submerged rectangular block not extending down to the bottom and fully submerged block extending down to the bottom with a finite gap are considered. An appropriate multi-term Galekin approximation technique involving ultraspherical Gegenbauer polynomial is employed for solving the integral equations arising in the mathematical analysis. The reflection and transmission coefficients of the progressive waves for two-dimensional time har- monic motion are evaluated by utilizing linearized potential theory. The theoretical result is validated numerically and explained graphically in a number of figures. The present result will almost match analytically and graphically with those results already available in the literature without considering the effect of surface tension. From the graphical representation, it is clearly visible that the amplitude of reflection coefficient decreases with increasing values of surface tension. It is also seen that the presence of surface tension, the change of width, and the height of the thick barriers affect the nature of the reflection coefficients significantly

Reflection and Transmission of Rayleigh Surface Waves by a Material Interphase

1991 ◽  
Vol 58 (3) ◽  
pp. 688-694 ◽  
Author(s):  
Z. L. Li ◽  
J. D. Achenbach
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Thin Layer ◽  
Surface Waves ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Mathematical Statement ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Rayleigh Surface Waves

Reflection and transmission of Rayleigh surface waves by a juncture normal to the free surface, between identical or different materials, has been investigated. The juncture, which may be an interface containing defects or a thin layer, is represented by a layer of extensional and shear springs. The mathematical statement of the problem is reduced to a system of singular integral equations for the displacements on the free surface and the tractions and the displacements across the juncture. Numerical solutions of this system have been computed by the use of the boundary element method. Expressions for the reflection and transmission coefficients have subsequently been obtained by the use of half-plane Green’s functions in conjunction with an elastodynamic representation integral. Results are presented for selected values of the elastic constants of the joined bodies and the stiffness parameters of the juncture.

A Combined Finite and Spectral Element Approach to Wave Scattering in a Cracked Beam: Modelling and Validation

2005 ◽  
Vol 293-294 ◽  
pp. 541-548 ◽  
Author(s):  
Simon P. Shone ◽  
Brian R. Mace ◽  
Tim P. Waters
Keyword(s):  
Wave Motion ◽  
Spectral Element ◽  
Experimental Results ◽  
Assessment Procedure ◽  
Fe Model ◽  
Cracked Beam ◽  
Combined Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Element Approach

This paper concerns flexural and axial wave motion in a cracked beam. A combined finite element (FE) and spectral element (SE) model of a cracked beam is presented. A portion of the beam, which contains the crack, is modelled using FE analysis and combined with semi-infinite SEs. From the combined model the reflection and transmission coefficients of the crack are estimated. To determine the accuracy of this approach, a beam with a mass discontinuity is considered in the first instance. The reflection coefficients are estimated numerically and compared with experimental results. Secondly, a slot-type transverse crack is cut along the width of the beam. The experimental results are compared with both an FE model and a conventional lumpedparameter spring model. The purpose of this work is to investigate further the use of audiofrequency wave propagation as a basis for crack assessment and provide a valid model to use in the development of an assessment procedure.

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