Dispersive properties of a fluid layer overlying a semi-infinite elastic solid*

1954 ◽  
Vol 44 (3) ◽  
pp. 493-512
Author(s):  
Ivan Tolstoy
Keyword(s):  
Elastic Body ◽  
Group Velocity ◽  
Normal Mode ◽  
Fundamental Mode ◽  
Fluid Layer ◽  
Elastic Solid ◽  
Numerical Results ◽  
Stoneley Wave ◽  
Wave Velocities ◽  
Minimum Group

Abstract The dispersive properties of waves propagating in a system consisting of a fluid layer overlying a semi-infinite elastic body are investigated by means of new formulas for the group velocity. The distribution of stationary values of the group velocity is examined in the light of these formulas and of numerical results. Also it is shown that the minimum group velocity of the fundamental mode may belong either to the normal-mode branch or to the Stoneley-wave branch, depending on the contrast in wave velocities between the two media.

scholarly journals PROPAGATION OF EXPLOSIVE SOUND IN A LIQUID LAYER OVERLYING A SEMI‐INFINITE ELASTIC SOLID

Geophysics ◽  
1950 ◽  
Vol 15 (3) ◽  
pp. 426-446 ◽  
Author(s):  
Frank Press ◽  
Maurice Ewing
Keyword(s):  
Phase Velocity ◽  
Pressure Distribution ◽  
Group Velocity ◽  
Normal Mode ◽  
Liquid Layer ◽  
Elastic Solid ◽  
Mode Propagation ◽  
Vertical Pressure ◽  
Velocity Amplitude ◽  
Incoming Signal

The Pekeris theory of normal mode propagation of explosion sound in two liquid layers is extended to include the case of a solid bottom. Curves giving phase velocity, group velocity, amplitude, vertical pressure distribution as a function of frequency are presented. The relative merits of geophones and hydrophones for underwater seismology and the best depth for each type of instrument are discussed in the light of the theory. The characteristics of an incoming signal are described.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

A Numerical Analysis for Cracks Emanating from a Quarter-Spherical Cavity on the Edge of an Elastic Body

2012 ◽  
Vol 499 ◽  
pp. 243-247
Author(s):  
Long Hai Yan ◽  
Bao Liang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Elastic Body ◽  
Spherical Cavity ◽  
Numerical Results ◽  
Shielding Effect ◽  
Corner Crack ◽  
Element Method

This note is specifically concerned with cracks emanating from a quarter-spherical cavity on the edge in an elastic body (see Fig.1) by using finite element method. The numerical results show that the existence of the cavity has a shielding effect of the corner crack. In addition, it is found that the effect of boundaries parallel to the crack on the SIFs is obvious when.H/R≤3

scholarly journals Sensitivities of surface wave velocities to the medium parameters in a radially anisotropic spherical Earth and inversion strategies

2015 ◽  
Vol 58 (5) ◽  
Author(s):  
Sankar N. Bhattacharya
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Love Waves ◽  
P Wave ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Wave Velocities ◽  
Spherical Earth

<p>Sensitivity kernels or partial derivatives of phase velocity (<em>c</em>) and group velocity (<em>U</em>) with respect to medium parameters are useful to interpret a given set of observed surface wave velocity data. In addition to phase velocities, group velocities are also being observed to find the radial anisotropy of the crust and mantle. However, sensitivities of group velocity for a radially anisotropic Earth have rarely been studied. Here we show sensitivities of group velocity along with those of phase velocity to the medium parameters <em>V<sub>SV</sub>, V<sub>SH </sub>, V<sub>PV</sub>, V<sub>PH , </sub></em><em>h</em><em> </em>and density in a radially anisotropic spherical Earth. The peak sensitivities for <em>U</em> are generally twice of those for <em>c</em>; thus <em>U</em> is more efficient than <em>c</em> to explore anisotropic nature of the medium. Love waves mainly depends on <em>V<sub>SH</sub></em> while Rayleigh waves is nearly independent of <em>V<sub>SH</sub></em> . The sensitivities show that there are trade-offs among these parameters during inversion and there is a need to reduce the number of parameters to be evaluated independently. It is suggested to use a nonlinear inversion jointly for Rayleigh and Love waves; in such a nonlinear inversion best solutions are obtained among the model parameters within prescribed limits for each parameter. We first choose <em>V<sub>SH</sub></em>, <em>V<sub>SV </sub></em>and <em>V<sub>PH</sub></em> within their corresponding limits; <em>V<sub>PV</sub></em> and <em>h</em> can be evaluated from empirical relations among the parameters. The density has small effect on surface wave velocities and it can be considered from other studies or from empirical relation of density to average P-wave velocity.</p>

Polarization-Insensitive Holey Fiber with Ultra-Small Mode Areas Using a Cross-Slot-Structure Core

2014 ◽  
Vol 609-610 ◽  
pp. 775-778
Author(s):  
Guan Jun Wang ◽  
Zhi Bin Wang ◽  
You Hua Chen ◽  
Yuan Yuan Chen ◽  
Yong Quan An ◽  
...  
Keyword(s):  
Group Velocity ◽  
Fundamental Mode ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Nonlinear Dispersion ◽  
Holey Fiber ◽  
Polarization Insensitive ◽  
Simulation Results ◽  
Hybrid Nanofiber ◽  
Slot Structure

A high nonlinear, dispersion flattened hybrid nanofiber with a silicon/silica cross-slot-structure nanocore is firstly proposed and analyzed, which is insensitive to polarization for implementing quasi-TE and quasi-TM fundamental modes transmission due to cross slot effect. Simulation results show that fundamental mode of ultra-small mode effective areas and high nonlinearity at TE and TM polarizations, which are confined in the narrow cross slot by four silicon ribs, can be achieved via this cross sot structure core. Moreover, the cladding of four large-air-holes promotes tailoring the group velocity dispersion (GVD) and enhancing nonlinearity furthermore. Our results indicate that ultra-small Aeff of 0.098μm2 and flat anomalous GVD with less than 13.5 ps.km-1.nm-1 dispersion ripple at C-band are realizable.

Vertical open fractures and shear‐wave velocities derived from VSPs, full waveform acoustic logs, and televiewer data

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 818-834 ◽  
Author(s):  
Frédéric Lefeuvre ◽  
Roger Turpening ◽  
Carol Caravana ◽  
Andrea Born ◽  
Laurence Nicoletis
Keyword(s):  
Shear Wave ◽  
Azimuthal Anisotropy ◽  
Stoneley Wave ◽  
Correlation Technique ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Full Waveform ◽  
Zero Offset

Fracture or stress‐related shear‐wave birefringence (or azimuthal anisotropy) from vertical seismic profiles (VSPs) is commonly observed today, but no attempt is made to fit the observations with observed in‐situ fractures and velocities. With data from a hard rock (limestones, dolomites, and anhydrites) region of Michigan, fast and slow shear‐wave velocities have been derived from a nine‐component zero offset VSP and compared to shear‐wave velocities from two full waveform acoustic logs. To represent the shear‐wave birefringence that affects the shear wave’s vertical propagation, a propagator matrix technique is used allowing a local measurement independent of the overburden layers. The picked times obtained by using a correlation technique have been corrected in the birefringent regions before we compute the fast and slow velocities. Although there are some differences between the three velocity sets, there is a good fit between the velocities from the shear‐wave VSP and those from the two logs. We suspect the formations showing birefringence to be vertically fractured. To support this, we examine the behavior of the Stoneley wave on the full waveform acoustic logs in the formations. In addition, we analyze the borehole televiewer data from a nearby well. There is a good fit between the fractures seen from the VSP data and those seen from the borehole.

CFD Simulations of Flow and Heat Transfer Through the Porous Interface of a Metal Foam Heat Exchanger

2014 ◽  
Author(s):  
Emilie Sauret ◽  
Kamel Hooman ◽  
Suvash C. Saha
Keyword(s):  
Numerical Modelling ◽  
Heat Recovery ◽  
Waste Heat Recovery ◽  
Metal Foam ◽  
Waste Heat ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Numerical Results ◽  
Waste Heat Recovery System ◽  
Porous Interface

This paper offers numerical modelling of a waste heat recovery system. A thin layer of metal foam is attached to a cold plate to absorb heat from hot gases leaving the system. The heat transferred from the exhaust gas is then transferred to a cold liquid flowing in a secondary loop. Two different foam PPI (Pores Per Inch) values are examined over a range of fluid velocities. Numerical results are then compared to both experimental data and theoretical results available in the literature. Challenges in getting the simulation results to match those of the experiments are addressed and discussed in detail. In particular, interface boundary conditions specified between a porous layer and a fluid layer are investigated. While physically one expects much lower fluid velocity in the pores compared to that of free flow, capturing this sharp gradient at the interface can add to the difficulties of numerical simulation. The existing models in the literature are modified by considering the pressure gradient inside and outside the foam. Comparisons against the numerical modelling are presented. Finally, based on experimentally-validated numerical results, thermo-hydraulic performance of foam heat exchangers as waste heat recovery units is discussed with the main goal of reducing the excess pressure drop and maximising the amount of heat that can be recovered from the hot gas stream.

A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction

2011 ◽  
Vol 10 (2) ◽  
pp. 279-304 ◽  
Author(s):  
J. W. Banks ◽  
B. Sjögreen
Keyword(s):  
Stability Analysis ◽  
Normal Mode ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Interface Condition ◽  
Finite Difference Schemes ◽  
Interface Conditions ◽  
Characteristic Boundary ◽  
Mode Stability ◽  
The Stability

AbstractIn multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocity- and stress-continuity can be enforced in the discrete approximation. This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes. The analysis shows that depending on the ratio of densities between the solid and the fluid, some numerical interface conditions are stable up to the maximal CFL-limit, while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit. The paper also presents a new interface condition, obtained as a simplified characteristic boundary condition, that is proved to not suffer from any reduction of the stable CFL-limit. Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.

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