High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Understanding Micro- and Macro-Mechanics of Soil Liquefaction: A Necessary Step for Field-Scale Assessment

Liquefaction is a devastating instability associated with saturated, loose, and cohesionless soils. It poses a significant risk to distributed infrastructure systems that are vital for the security, economy, safety, health, and welfare of societies. In order to make our cities resilient to the effects of liquefaction, it is important to be able to identify areas that are most susceptible. Some of the prevalent methodologies employed to identify susceptible areas include conventional slope stability analysis and the use of so-called liquefaction charts. However, these methodologies have some limitations, which motivate our research objectives. In this dissertation, we investigate the mechanics of origin of liquefaction in a laboratory test using grain-scale simulations, which helps (i) understand why certain soils liquefy under certain conditions, and (ii) identify a necessary precursor for onset of flow liquefaction. Furthermore, we investigate the mechanics of liquefaction charts using a continuum plasticity model; this can help in modeling the surface hazards of liquefaction following an earthquake. Finally, we also investigate the microscopic definition of soil shear wave velocity, a soil property that is used as an index to quantify liquefaction resistance of soil. We show that anisotropy in fabric, or grain arrangement can be correlated with anisotropy in shear wave velocity. This has the potential to quantify the effects of sample disturbance when a soil specimen is extracted from the field. In conclusion, by developing a more fundamental understanding of soil liquefaction, this dissertation takes necessary steps for a more physical assessment of liquefaction susceptibility at the field-scale.

Thermal stress-induced birefringence in borate glass irradiated by femtosecond laser pulses

Thermal stress-induced birefringence in borate glass which has been irradiated by 800-nm femtosecond laser pulses is observed under cross-polarized light. Due to the high temperature and pressure formed in the focal volume, the material at the edge of the micro-modified region is compressed between the expanding region and the unheated one, then stress emerges. Raman spectroscopy is used to investigate the stress distribution in the micro-modified region and indicates the redistributions of density and refractive index by Raman peak shift. We suggest that this technique can develop waveguide polarizers and Fresnel zone plates in integrated optics.

The effect of nozzle design on laser micro-machining of M2 tool steels

This paper shows how computational techniques have been used to develop axi-symmetric, straight, sonic-line, minimum length micro nozzles that are suitable for laser micro-machining applications. Gas jets are used during laser micro-machining processing applications to shield the interaction zone between laser and workpiece material, and they determine the machining efficiency of such applications. The paper discusses the nature of laser-material interactions and the importance of using computational fluid dynamics to model pressure distributions in short nozzles that are used to deliver gas to the laser-material interaction zone. Experimental results are presented that highlight unique problems associated with laser micro machining using gas jets.

The contact of rough surfaces carrying pressure sensitive boundary layers

When two rough surfaces are loaded together it is well known that the area of true contact is very much smaller then the geometric area and that, consequently, local contact pressures are very much greater than the nominal value. If the asperities on each surface can be thought of as possessing smooth summits and each of the solids is elastically isotropic then the pressure distribution will consist of a series of small, but severe, Hertzian patches. However, if one of both of the surfaces in question is protected by a boundary layer then both the number and dimensions of these patches, and the form of the pressure distribution within them, will be modified. Recent experimental evidence from studies using both Atomic Force Microscopy and micro-tribometry suggests that boundary films produced by the action of commercial anti-wear additives, such as ZDTP, exhibit mechanical properties, which are affected by local values of pressure. These changes bring about further modifications to local conditions. These effects have been explored in a numerical model of rough surface contact and the implications for the mechanisms of surface distress and wear are discussed. © 2000 Elsevier Science B.V. All rights reserved.

An experimental study of unsteady separated shock wave boundary layer interactions

An experimental investigation of the unsteady interaction between a turbulent boundary layer and a normal shock wave of strength M∞ = 1.4 subject to periodic forcing in a parallel walled duct has been conducted. Emphasis has been placed on the mechanism by which changes in the global flow field influence the local interaction structure. Static pressure measurements and high speed Schlieren images of the unsteady interaction have been obtained. The pressure rise across the interaction and the appearance of the local SBLI structure have been observed to vary during the cycle of periodic shock wave motion. The magnitude of the pressure rise across the interaction is found to be related to the relative Mach number of the unsteady shock wave as it undergoes periodic motion. Variations in the upstream Influence of the interaction are sensitive to the magnitude and direction of shock wave velocity and acceleration and it is proposed that a viscous lag exists between the point of boundary layer separation and the shock wave position. Further work exploring the implications of these findings is proposed, including studies of the variation in position of the points of boundary layer separation and reattachment.

Tsunami wave loading on coastal houses: A model approach

The Asian tsunami of 26 December 2004 killed over 220 000 people and devastated coastal structures, including many thousands of traditional brick-built homes. This paper presents the results of model tests that compare the impact of a tsunami wave on a typical coastal house with that on a new tsunami resistant design developed in the USA and now built in Sri Lanka Digital images recorded during the test reveal how the tsunami wave passed through the new house design without damaging it but severely damaged the typical coastal house. Pressure sensor results also provided further insight into tsunami wave loading, indicating that the established Japanese method significantly underestimates maximum impact load.

Performance of choked unsteady ejector-nozzles for use in pressure-gain combustors

If the conventional steady flow combustor of a gas turbine is replaced with a device which achieves a pressure gain during the combustion process then the thermal efficiency of the cycle is raised. All such 'Pressure Gain Combustors' (e.g. PDEs, pulse combustors or wave rotors) are inherently unsteady flow devices. For such a device to be practically installed in a gas turbine it is necessary to design a downstream row of turbine vanes which will both accept the combustors unsteady exit flow and deliver a flow which the turbine rotor can accept. The design requirements of such a vane are that its exit flow both retains the maximum time-mean stagnation pressure gain (the pressure gain produced by the combustor is not lost) and minimises the amplitude of unsteadiness (reduces unsteadiness entering the downstream rotor). In this paper the exit of the pressure gain combustor is simulated with a cold unsteady jet. The first stage vane is simulated by a one-dimensional choked ejector nozzle with no turning. The time-mean and rms stagnation pressure at nozzle exit is measured. A number of geometric configurations are investigated and it is shown that the optimal geometry both maximizes time mean stagnation pressure gain (75% of that in the exit of the unsteady jet) and minimizes the amplitude of unsteadiness (1/3 of that in the primary jet). The structure of the unsteady flow within the ejector nozzle is determined computationally. Copyright © 2009 by J Heffer and R Miller.

An experimental and numerical study of an oscillating transonic shock wave in a duct

A combined experimental and numerical study of a transonic shock wave in a parallel walled duct subject to downstream pressure perturbations has been conducted. Experiments and simulations have been carried out with a shock strength of M∞ = 1.4 for pressure perturbation frequencies in the range 16-90 Hz. The dynamics of unsteady shock motion and the interaction structure between the unsteady transonic shock wave and the turbulent tunnel floor boundary layer have been investigated. It is found that the (experimentally measured) dynamics of shock motion are generally well predicted by the computational scheme, especially at relatively low (≈ 40 Hz) frequencies. However, at higher frequencies (≈ 90 Hz), some subtle differences between the shock dynamics measured in experiments and those predicted by Computational Fluid Dynamics (CFD) exist. There is evidence from experiments that variations in shock / boundary layer interaction (SBLI) structure caused by shock motion are responsible for a change in the nature of shock dynamics between low and high frequency. In contrast, numerical results at low and high frequencies do not differ significantly and this suggests that the numerical method is not fully capturing the physics of the unsteady flow. Possible reasons for this are considered and a number of areas where CFD is unable to replicate experimental observations are identified. Significantly, CFD predicts changes in SBLI structure due to shock motion that are much too large and this may explain why none of the subtle effects on shock dynamics seen in experiments occur in CFD. Further work developing numerical methods that demonstrate a more realistic sensitivity of SBLI structure to unsteady shock motion is required. Copyright © 2010 by P.J.K. Bruce.

Simulation of solitary wave impact on coastal structures using weakly compressible and incompressible SPH methods

In this paper, we engage a Lagrangian, particle-based CFD method, named Smoothed Particle Hydrodynamic (SPH) to study the solitary wave motion and its impact on coastal structures. Two-dimensional weakly compressible and incompressible SPH models were applied to simulate wave impacting on seawall and schematic coastal house. The results confirmed the accuracy of both models for predicting the wave surface profiles. The incompressible SPH model performed better in predicting the pressure field and impact loadings on coastal structures than the weakly compressible SPH model. The results are in qualitatively agreement with experimental results. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Corner separation effects for normal shock wave/turbulent boundary layer interactions in rectangular channels

Experiments are conducted to examine the mechanisms behind the coupling between corner separation and separation away from the corner when holding a high-Machnumber M∞ = 1.5 normal shock in a rectangular channel. The ensuing shock wave interaction with the boundary layer on the wind tunnel floor and in the corners was studied using laser Doppler anemometry, Pitot probe traverses, pressure sensitive paint and flow visualization. The primary mechanism explaining the link between the corner separation size and the other areas of separation appears to be the generation of compression waves at the corner, which act to smear the adverse pressure gradient imposed upon other parts of the flow. Experimental results indicate that the alteration of the -region, which occurs in the supersonic portion of the shock wave/boundary layer interaction (SBLI), is more important than the generation of any blockage in the subsonic region downstream of the shock wave. © Copyright 2012 Cambridge University Press.

Influence of micro supersonic jets on micro percussion drilling of 316L stainless steel using nanosecond 355NM laser radiation

The interaction phenomena of nanosecond Q-switched diode-pumped solid state (DPSS) laser using 355nm radiation with 0.2mm thick 316L stainless steel foil was investigated at incident laser fluence range of 19 - 82Jcm-2. The characterization study was performed with and without the use of assist gas by utilizing micro supersonic minimum length nozzles (MLN), specifically designed for air at inlet chamber pressure of 8bar. MLN ranged in throat diameters of 200μm, 300μm, and 500μm respectively. Average etch rate per pulse under the influence of three micro supersonic impinging jets, for both oxygen and air showed the average etch rate was reduced when high-speed gas jets were utilized, compared to that without any gas jets, but significant variation was noticed between different jet sizes. Highest etch rate and quality was achieved with the smallest diameter nozzle, suggesting that micro nozzles can produce a viable process route for micro laser cutting.

Flaw sizing in pipes using long-range guided wave testing

The absence of adequate inspection data from difficult-to-access areas on pipelines, such as cased-road crossings, makes determination of fitness for continued service and compliance with increasingly stringent regulatory requirements problematic. Screening for corrosion using long-range guided wave testing is a relatively new inspection technique. The complexity of the possible modes of vibration means the technique can be difficult to implement effectively but this also means that it has great potential for both detecting and characterizing flaws. The ability to determine flaw size would enable the direct application of standard procedures for determining fitness-for-service, such as ASME B31G, RSTRENG, or equivalent for tens of metres of pipeline from a single inspection location. This paper presents a new technique for flaw sizing using guided wave inspection data. The technique has been developed using finite element models and experimentally validated on 6'' Schedule 40 steel pipe. Some basic fitness-for-service assessments have been carried out using the measured values and the maximum allowable operating pressure was accurately determined. © 2011 American Institute of Physics.

Control of a shock-wave/boundary-layer interaction and subsequent subsonic diffuser using a combination of vortex generators and bleed

An experimental investigation has been undertaken in which vortex generators (VGs) have been employed to inhibit boundary-layer separation produced by the combined adversepressure- gradient of a terminal shock-wave and subsonic diffuser. This setup has been developed as part of a program to produce a more inlet relevant flow-field using a small-scale wind tunnel than previous studies. The resulting flow is dominated by large-scale separation, and as such, is thought to be a good test-bed for flow control. In this investigation, VGs have been added to determine their potential for shock-induced separation mitigation. In line with previous studies, it was observed that the application of VGs alone was not able to significantly alleviate separation overall, because enlarged corner separations was observed. Only when control of the corner separations using corner bleed was employed alongside centre-span control using VGs was a significant improvement in both wall pressure recovery (6% increase) and stagnation pressure recovery (2.4% increase) observed. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.

Shock wave/boundary-layer interaction control using a combination of vortex generators and bleed

To investigate whether vortex generators can be an effective form of passive flow control an experimental investigation has been conducted in a small-scale wind tunnel. With specific emphasis on supersonic inlet applications flow separation was initiated using a combined terminal shock wave and subsonic diffuser: a configuration that has been developed as a part of a program to produce a more inlet-relevant flowfield in a small-scale wind tunnel than previous studies. When flow control was initially introduced little overall flow improvement was obtained as the losses tended to be redistributed instead of removed. It became apparent that there existed a strong coupling between the center-span flow and the corner flows. As a consequence, only when flow control was applied to both the corner flows and center-span flow was a significant flow improvement obtained. When corner suction and center-span vortex generators were employed in tandem separation was much reduced and wall-pressure and stagnation pressure were notably improved. As a result, when applied appropriately, it is thought that vortex generators do have the potential to reduce the dependence on boundary-layer bleed for the purpose of separation suppression. Copyright © 2012 by Neil Titchener and Holger Babinsky. Published by the American Institute of Aeronautics and Astronautics, Inc.