The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Estudo teórico e experimental da velocidade do som em sistemas contendo hidrocarbonetos

A descoberta de reservatórios de petróleo na camada do pré-sal abriu novas perspectivas para a economia brasileira. A grandes profundidades, com elevado teor de CO2 e submetidos a altas pressões e temperaturas, a exploração de petróleo das camadas de pré-sal constitui um considerável desafio tecnológico. Neste contexto, o conhecimento dos coeficientes de compressibilidade são fundamentais para o estudo do comportamento termodinâmico e escoamento dos fluidos destes campos de produção. Com este objetivo, foram determinadas experimentalmente nesta dissertação a massa específica e a velocidade do som de sistemas envolvendo quatro hidrocarbonetos puros: n-decano, n-hexadecano, decalina e tetralina, assim como para sistemas multicompostos envolvendo estes hidrocarbonetos e para uma amostra de condensado de petróleo. Os resultados obtidos permitiram o cálculo dos coeficientes de compressibilidade isentrópica, isotérmica e isentálpica. É apresentada uma avaliação sobre a capacidade de se correlacionar dados experimentais de velocidade do som aos dados calculados pelas equações de estado de Peng-Robinson e Lee-Kesler com regras de mistura: (i) Spencer e Danner e (ii) Lee-Kesler

Estudo da inspeção e caracterização de materiais compósitos por ultrassom

O presente trabalho foi desenvolvido com o intuito de estudar a utilização do método de ensaio não destrutivo de ultrassom para inspecionar e caracterizar materiais compósitos. Os objetivos principais da pesquisa foram medir a espessura, encontrar e dimensionar delaminações em reparo de material compósito laminado para tubulações e medir a velocidade do som no concreto para o cálculo do módulo de elasticidade. Inicialmente foram estudados os parâmetros físicos relevantes inerentes a cada material para o método de ultrassom, para então estabelecer uma metodologia de inspeção. A técnica de pulso-eco foi capaz de encontrar as descontinuidades no compósito laminado. Para a determinação do módulo de elasticidade do concreto, a técnica de transmissão foi utilizada obtendo-se resultados satisfatórios.

Stratigraphic Model Predictions of Geoacoustic Properties

Geoacoustic properties of the seabed have a controlling role in the propagation and reverberation of sound in shallow-water environments. Several techniques are available to quantify the important properties but are usually unable to adequately sample the region of interest. In this paper, we explore the potential for obtaining geotechnical properties from a process-based stratigraphic model. Grain-size predictions from the stratigraphic model are combined with two acoustic models to estimate sound speed with distance across the New Jersey continental shelf and with depth below the seabed. Model predictions are compared to two independent sets of data: 1) Surficial sound speeds obtained through direct measurement using in situ compressional wave probes, and 2) sound speed as a function of depth obtained through inversion of seabed reflection measurements. In water depths less than 100 m, the model predictions produce a trend of decreasing grain-size and sound speed with increasing water depth as similarly observed in the measured surficial data. In water depths between 100 and 130 m, the model predictions exhibit an increase in sound speed that was not observed in the measured surficial data. A closer comparison indicates that the grain-sizes predicted for the surficial sediments are generally too small producing sound speeds that are too slow. The predicted sound speeds also tend to be too slow for sediments 0.5-20 m below the seabed in water depths greater than 100 m. However, in water depths less than 100 m, the sound speeds between 0.5-20-m subbottom depth are generally too fast. There are several reasons for the discrepancies including the stratigraphic model was limited to two dimensions, the model was unable to simulate biologic processes responsible for the high sound-speed shell material common in the model area, and incomplete geological records necessary to accurately predict grain-size

INVESTIGATION OF OCEAN ACOUSTICS USING AUTONOMOUS INSTRUMENTATION TO QUANTIFY THE WATER-SEDIMENT BOUNDARY PROPERTIES

Sound propagation in shallow water is characterized by interaction with the oceans surface, volume, and bottom. In many coastal margin regions, including the Eastern U.S. continental shelf and the coastal seas of China, the bottom is composed of a depositional sandy-silty top layer. Previous measurements of narrow and broadband sound transmission at frequencies from 100 Hz to 1 kHz in these regions are consistent with waveguide calculations based on depth and frequency dependent sound speed, attenuation and density profiles. Theoretical predictions for the frequency dependence of attenuation vary from quadratic for the porous media model of M.A. Biot to linear for various competing models. Results from experiments performed under known conditions with sandy bottoms, however, have agreed with attenuation proportional to f1.84, which is slightly less than the theoretical value of f2 [Zhou and Zhang, J. Acoust. Soc. Am. 117, 2494]. This dissertation presents a reexamination of the fundamental considerations in the Biot derivation and leads to a simplification of the theory that can be coupled with site-specific, depth dependent attenuation and sound speed profiles to explain the observed frequency dependence. Long-range sound transmission measurements in a known waveguide can be used to estimate the site-specific sediment attenuation properties, but the costs and time associated with such at-sea experiments using traditional measurement techniques can be prohibitive. Here a new measurement tool consisting of an autonomous underwater vehicle and a small, low noise, towed hydrophone array was developed and used to obtain accurate long-range sound transmission measurements efficiently and cost effectively. To demonstrate this capability and to determine the modal and intrinsic attenuation characteristics, experiments were conducted in a carefully surveyed area in Nantucket Sound. A best-fit comparison between measured results and calculated results, while varying attenuation parameters, revealed the estimated power law exponent to be 1.87 between 220.5 and 1228 Hz. These results demonstrate the utility of this new cost effective and accurate measurement system. The sound transmission results, when compared with calculations based on the modified Biot theory, are shown to explain the observed frequency dependence.

EXPERIMENTAL INVESTIGATION OF LINEAR BUBBLE DYNAMICS IN A VISCOELASTIC XANTHAN GEL

Oceanic bubble plumes caused by ship wakes or breaking waves disrupt sonar communi- cation because of the dramatic change in sound speed and attenuation in the bubbly fluid. Experiments in bubbly fluids have suffered from the inability to quantitatively characterize the fluid because of continuous air bubble motion. Conversely, single bubble experiments, where the bubble is trapped by a pressure field or stabilizing object, are limited in usable frequency range, apparatus complexity, or the invasive nature of the stabilizing object (wire, plate, etc.). Suspension of a bubble in a viscoelastic Xanthan gel allows acoustically forced oscilla- tions with negligible translation over a broad frequency band. Assuming only linear, radial motion, laser scattering from a bubble oscillating below, through, and above its resonance is measured. As the bubble dissolves in the gel, different bubble sizes are measured in the range 240 – 470 μm radius, corresponding to the frequency range 6 – 14 kHz. Equalization of the cell response in the raw data isolates the frequency response of the bubble. Compari- son to theory for a bubble in water shows good agreement between the predicted resonance frequency and damping, such that the bubble behaves as if it were oscillating in water.

A FLOW-THROUGH ACOUSTIC WAVEGUIDE FOR TWO-PHASE BUBBLY FLOW VOID FRACTION MEASUREMENT

In the Spallation Neutron Source (SNS) facility at Oak Ridge National Laboratory (ORNL), the deposition of a high-energy proton beam into the liquid mercury target forms bubbles whose asymmetric collapse cause Cavitation Damage Erosion (CDE) to the container walls, thereby reducing its usable lifetime. One proposed solution for mitigation of this damage is to inject a population of microbubbles into the mercury, yielding a compliant and attenuative medium that will reduce the resulting cavitation damage. This potential solution presents the task of creating a diagnostic tool to monitor bubble population in the mercury flow in order to correlate void fraction and damage. Details of an acoustic waveguide for the eventual measurement of two-phase mercury-helium flow void fraction are discussed. The assembly’s waveguide is a vertically oriented stainless steel cylinder with 5.08cm ID, 1.27cm wall thickness and 40cm length. For water experiments, a 2.54cm thick stainless steel plate at the bottom supports the fluid, provides an acoustically rigid boundary condition, and is the mounting point for a hydrophone. A port near the bottom is the inlet for the fluid of interest. A spillover reservoir welded to the upper portion of the main tube allows for a flow-through design, yielding a pressure release top boundary condition for the waveguide. A cover on the reservoir supports an electrodynamic shaker that is driven by linear frequency sweeps to excite the tube. The hydrophone captures the frequency response of the waveguide. The sound speed of the flowing medium is calculated, assuming a linear dependence of axial mode number on modal frequency (plane wave). Assuming that the medium has an effective-mixture sound speed, and that it contains bubbles which are much smaller than the resonance radii at the highest frequency of interest (Wood’s limit), the void fraction of the flow is calculated. Results for water and bubbly water of varying void fraction are presented, and serve to demonstrate the accuracy and precision of the apparatus.

AN IMPEDANCE TUBE FOR THE IN-SITU CLASSIFICATION OF BUBBLY LIQUIDS

It is well documented that the presence of even a few air bubbles in water can signifi- cantly alter the propagation and scattering of sound. Air bubbles are both naturally and artificially generated in all marine environments, especially near the sea surface. The abil- ity to measure the acoustic propagation parameters of bubbly liquids in situ has long been a goal of the underwater acoustics community. One promising solution is a submersible, thick-walled, liquid-filled impedance tube. Recent water-filled impedance tube work was successful at characterizing low void fraction bubbly liquids in the laboratory [1]. This work details the modifications made to the existing impedance tube design to allow for submersed deployment in a controlled environment, such as a large tank or a test pond. As well as being submersible, the useable frequency range of the device is increased from 5 - 9 kHz to 1 - 16 kHz and it does not require any form of calibration. The opening of the new impedance tube is fitted with a large stainless steel flange to better define the boundary condition on the plane of the tube opening. The new device was validated against the classic theoretical result for the complex reflection coefficient of a tube opening fitted with an infinite flange. The complex reflection coefficient was then measured with a bubbly liquid (order 250 micron radius and 0.1 - 0.5 % void fraction) outside the tube opening. Results from the bubbly liquid experiments were inconsistent with flanged tube theory using current bubbly liquid models. The results were more closely matched to unflanged tube theory, suggesting that the high attenuation and phase speeds in the bubbly liquid made the tube opening appear as if it were radiating into free space.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

The Origin of Type I Spicule Oscillations

We use images of high spatial and temporal resolution, obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope, to reveal how the generation of transverse waves in Type I spicules is a direct result of longitudinal oscillations occurring in the photosphere. Here we show how pressure oscillations, with periodicities in the range of 130–440 s, manifest in small-scale photospheric magnetic bright points, and generate kink waves in the Sun’s outer atmosphere with transverse velocities approaching the local sound speed. Through comparison of our observations with advanced two-dimensional magnetohydrodynamic simulations, we provide evidence for how magnetoacoustic oscillations, generated at the solar surface, funnel upward along Type I spicule structures, before undergoing longitudinal-to-transverse mode conversion into waves at twice the initial driving frequency. The resulting kink modes are visible in chromospheric plasma, with periodicities of 65–220 s, and amplitudes often exceeding 400 km. A sausage mode oscillation also arises as a consequence of the photospheric driver, which is visible in both simulated and observational time series. We conclude that the mode conversion and period modi?cation is a direct consequence of the 90? phase shift encompassing opposite sides of the photospheric driver. The chromospheric energy ?ux of these waves are estimated to be ˜3 × 105 W m-2, which indicates that they are suf?ciently energetic to accelerate the solar wind and heat the localized corona to its multi-million degree temperatures.

The plasma mirror - A subpicosecond optical switch for ultrahigh power lasers

Plasma mirrors are devices capable of switching very high laser powers on subpicosecond time scales with a dynamic range of 20–30 dB. A detailed study of their performance in the near-field of the laser beam is presented, a setup relevant to improving the pulse contrast of modern ultrahigh power lasers ~TW–PW!. The conditions under which high reflectivity can be achieved and focusability of the reflected beam retained are identified. At higher intensities a region of high specular reflectivity with rapidly decreasing focusability was observed, suggesting that specular reflectivity alone is not an adequate guide to the ideal range of plasma mirror operation. It was found that to achieve high reflectivity with negligible phasefront distortion of the reflected beam the inequality csDt,lLaser must be met (cs : sound speed, Dt: time from plasma formation to the peak of the pulse!. The achievable contrast enhancement is given by the ratio of plasma mirror reflectivity to cold reflectivity.

Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma

The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included.

Acoustic-oceanographic data fusion for prediction of oceanic acoustic elds

Tese de doutoramento, Engenharia Electrónica e Telecomunicações (Processamento de Sinal), Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2014

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.