Adiabatic Propagation Research Articles

Patterns of time propagation on the grid of potential curves

Time-propagation patterns are studied for a network formed by two bands of equidistant rectilinear parallel diabatic potential curves that cross each other. In the case of weak coupling between the bands the propagation proceeds mostly via a diabatic path. In the case of strong coupling a different regime of antidiabatic propagation is revealed. For the intermediate case of coupling strength the propagation is basically described by an overlay of diabatic and antidiabatic patterns; interestingly, the adiabatic propagation is never operative. The present dynamic quantum model is compared with those models that assume a reduction of the problem to a succession of pairwise transitions between the states.

Gaseous-Propellant Microthrusters. II. Venting Prior to Completion of Burn

We present results from an inviscid one-dimensional model of the quasi-steady adiabatic dame propagation within a closed cylindrical container, as a consequence of a localized ignition in an initially homogeneous and quiescent mixture of reactive ideal gases. We continue the description after the instantaneous removal of an effectively massless diaphragm permits discharge from a sonic orifice, located at either the ignition end or the opposite end of the container. In a companion study (part I, published separately), the efflux begins only after the burn of the contents is complete; here, in contrast, the diaphragm is instantaneously removed when a pressure is achieved which is less than the adiabatic pressure for complete combustion of the contents. Key results include the temporal histories of the fraction of the initial mass that is burned within the container, the fraction of the initial mass that has exited the container, and the flux of momentum associated with the efflux of mass (for the case in which the container itself does not move). For cases of interest, involving a single simple hydrocarbon vapor in a fuel-lean mixture with oxygen and a diluent, at an initial pressure in excess of one atmosphere, the pressure increases mono-tonically (and appreciably) until diaphragm rupture; thereafter, the pressure typically decreases with efflux, and the flame speed across the mixture typically increases with the decreasing pressure. Thus, flameout (so the combustion within the container of the initial contents is incomplete) is neither coincident with diaphragm rupture nor owing to a chemical-kinetic consequence of the decrease of the (spatially virtually uniform) pressure. Rather, flameout is owing to the efflux of all hot burned gas from the container, so there is no preheating of residual cold unburned mixture to sustain propagation of the deflagration within the container.

Remarks on impact shearing

A review is presented on recent progress in shear testing of materials at high and very high strain rates. Some experimental techniques are discussed which allow for materials testing in shear up to 10 6 l\\s. More detailed informations are provided on experimental techniques based on the Modified Double Shear specimen loaded by direct impact. This technique has been applied so far to test a variety of materials, including construction, armor and inoxidable steels, and also aluminum alloys. The double shear configuration has also been applied to test sheet metals, mostly used in the automotive industry, in a wide range of strain rates. Details of both techniques, including measuring systems and elastic wave propagation in tubes, are discussed. In addition, a new experimental configuration which can be applied for experimental studies of adiabatic shear propagation and high speed machining is discussed. The role of adiabatic heating at different rates of shearing is also discussed, including transition from pure isothermal to pure adiabatic deformation. It appears that the initial impact velocity is an important parameter in development of plastic localization. Finally, a new development is discussed in determination of the Critical Impact Velocity in shear. A comparison is shown between recent experimental findings and a simple analytic estimation. The CIV in shear is a certain mode of adiabatic failure which occurs at relatively high shear velocities of adjacent material layers. Numerical simulations support the existence of the CIV in shear which can be recognized to some extent as a material constant.

Improving a practical broadband adiabatic normal mode model by including untrapped modes

An adiabatic normal mode model that neglects untrapped mode contributions will give inaccurate transmission loss predictions for environments with bottom slopes when modes transition between being trapped and untrapped. For example, initially untrapped, but strongly excited, modes that subsequently become trapped away from the source may contribute significantly to water column fields. Results of Tindle and Zhang [Oceans ’93 Proceedings, I-81] show that including untrapped modes in an adiabatic description significantly improves transmission loss predictions for the ASA benchmark wedge problem. A practical implementation of an adiabatic broadband propagation model for both trapped and untrapped modes will be described. Difficulties associated with the transition region between trapped and untrapped modes near the critical angle will be discussed, and the results of inserting a gradient in the lower half-space to solve the problem will be presented. [Work supported by ONR.]

Pulsating instability in near-limit propagation of rich hydrogen/air flames

The adiabatic and radiation-affected unsteady planar propagation of rich hydrogen/air flames of nearlimit concentrations in the doubly infinite domain is computationally simulated with detailed chemistry and transport. Results for the adiabatic propagation show that, with progressive increase in the fuel richness, the mode of propagation changes from steady state to oscillatory with a single period, to oscillatory with double periods, and to oscillation separated by increasingly long periods of dormant chemical reactivity. In the presence of radiative loss, propagation with the first three modes are minimally affected, whereas extinction readily occurs, with precipitous drop in the flame temperature, during the dormant period of the last mode. Because the state for the onset of the last mode is at a leaner concentration than that of the nonadiabatic steady-state propagation limit the use of the steady-state result provides a conservative estimate for the rich fundamentall flammability limit. The study also shows that, by using appropriately extracted Lewis and Zeldovich numbers characterizing the steady, adiabatic flame propagation, the transition boundary from steady to pulsating propagation can be adequately described by the criterion derived by Sivashinsky based on one-step chemistry.

Deflagration and detonation in solid‐solid combustion

AbstractSolid‐solid combustion becomes self‐sustaining when the preheating of the fresh mixture is high enough to support a spontaneous chemical reaction. These reactions have high activation energies, requiring significant preheating. Traditionally, conduction has been considered as the main form of preheating, and propagation velocities in the order of a few mm to a few cm per second were found. When acoustic equations are included in the analysis, no significant changes occur for traditional SHS reactions. However, the analysis of a 1‐D model propagating at a constant velocity reveals the existence of two other solutions with propagation velocities which are much faster. An SHS deflagration wave is found with combustion temperature lower than the adiabatic value. The propagation velocity is less than the longitudinal sound speed of the medium, but typical Mach numbers vary between 0.6 and 0.95. The third solution is an SHS detonation with temperature above the adiabatic value and supersonic propagation velocity. Since the heat fluxes are extremely high, the hyperbolic conduction model is used.

Nonlinear wide-angle paraxial acoustic propagation in shallow-water channels

A time-domain model that describes wide-angle paraxial propagation of acoustic pulses in shallow water is developed. This model incorporates weak nonlinear effects and depth variability in both ambient density and sound speed. Derivations of paraxial approximations are based on an iterative approach, in which the wide-angle approximation is obtained by using a narrow-angle equation to approximate the second range derivative in the two-way equation. Scaling arguments are used to obtain a more tractable simplification of the equation. The wide-angle equation is solved numerically by splitting into components representing distinct physical processes and using a modified version of the time-domain parabolic equation (TDPE) code [M. D. Collins, J. Acoust. Soc. Am. 84, 2114–2125 (1988)]. A high-order upwind flux-correction method is modified to handle the nonlinear component. Numerical results are presented for adiabatic propagation in a shallow, isospeed channel. It is demonstrated that nonlinear effects are significant, even at small ranges, if the peak source pressure is high enough. Both nonlinear and wide-angle effects are illustrated, and their differences are discussed.

Adiabatic Phase Boundary Propagation in a Theromoelastic Solid

The dynamical aspects of solid-solid phase transformations are studied within the framework of the theory of thermoelasticity. A problem of the Riemann type for a one-dimensional bar undergoing an adiabatic process is analyzed. It is shown that by imposing a kinetic relation and a nucleation criterion, it is possible to single out a unique solution. This extends to the thermomechanical case results previously found in a purely mechanical context.

Spatiotemporal bright soliton Y junctions in nonlinear planar waveguides

The splitting and steering of ultrashort pulses propagating through a Kerr medium are investigated. This investigation extends earlier ones of cw spatial soliton Y junctions into the area of subpicosecond solitonlike pulse propagation. Besides that of the all-optical steering process, the influence of normal group-velocity dispersion and two-photon absorption is discussed. It is found that both processes modify the transmission characteristics of the system (i.e., output versus input beam intensity) in a similar way. However, two-photon absorption inhibits the steering property of Y junctions, whereas normal group-velocity dispersion enhances it. A model based on an adiabatic propagation approximation is used to explain this behavior qualitatively.

Coupled acoustic mode propagation through continental-shelf internal solitary waves

Three techniques are used to investigate mode coupling as acoustic energy passes through continental-shelf internal solitary waves (ISW's). Results from all techniques agree. The waves considered here are single downward undulations of a thermocline layer separating upper and lower well-mixed layers. Two techniques are numerical: parabolic equation (PE) solution and a sudden approximation joining range-invariant regions at sharp vertical interfaces. The third technique is an analytic derivation of ISW scale lengths separating adiabatic (at large scale) and coupled-mode propagation. Results show that energy is exchanged between modes as ISW's are traversed. The sharp interface solutions help explain this in terms of spatially confined coupling and modal phase interference. Three regimes are observed: 1) for short ISW's, coupling upon wave entrance is reversed upon exit, with no net coupling; 2) for ISW scales of 75-200 m, modal phase alteration averts the exit reversal, giving net coupling; transparent resonances yielding no net coupling are also observed in this regime; and 3) for long ISW's, adiabaticity is probable but not universal. Mode refraction analysis for nonparallel acoustic-ISW alignment suggests that these two-dimensional techniques remain valid for 0/spl deg/ (parallel) to 65/spl deg/ (oblique) incidence, with an accordant ISW stretching.

Horizontal refraction tomography with mode interaction

Measurements of horizontal refraction angles associated with horizontal refraction of different acoustic modes can be used for inferring 3-D ocean inner structure [A. G. Voronovich and E. C. Shang, J. Acoust. Soc. Am. 98, 2708–2716 (1995)]. Numerical simulations demonstrated that the corresponding inversion scheme works very well for adiabatic propagation. It was also shown that the nonadiabatic case can be incorporated into the inversion scheme when mode interactions can be approximately accounted for by modifying local values of propagation constants of modes. In the present investigation, mode interaction is taken into account in a much more realistic ‘‘N×2-D’’ approximation (only relatively weak azimuth coupling is neglected). A new exact algorithm was used for the calculation of mode interactions in the plane of propagation. Numerical simulations showed that in many cases, the effect of mode interactions on horizontal refraction is rather weak and can be taken into account by rapidly converging iterative procedure. The results of tomography reconstruction of mesoscale inhomogeneities typical for the Pacific are demonstrated. [Work supported by ONR.]

Adiabatic propagation of distributions: Exactly solvable models.

Adiabatic propagation of distributions: Exactly solvable models.

Effects of random density fluctuations on matter-enhanced neutrino flavor transitions in supernovas and implications for supernova dynamics and nucleosynthesis.

We calculate the effects of random density fluctuations on two-neutrino flavor transformations (${\nu}_{\tau(\mu)} \rightleftharpoons {\nu}_e$) in the post-core-bounce supernova environment. In particular, we follow numerically the flavor evolution of neutrino states propagating through a stochastic field of density fluctuations. We examine the approach to neutrino flavor depolarization, and study the effects of this phenomenon in both the early shock reheating epoch and the later r-process nucleosynthesis epoch. Our results suggest that significant fluctuation-induced neutrino flavor depolarization effects occur in these environments only when the zero-order (without density fluctautions) evolution of the neutrino states includes adiabatic propagation through resonances (mass level crossings). In the shock reheating epoch, depolarization effects from fluctuations with amplitudes larger than 0.05% of the local matter density can cause an increase in the heating rate of the material behind the shock compared to the case with no neutrino flavor transformation - but this corresponds to a significant decrease in this quantity relative to the case with adiabatic neutrino transformation. If r-process nucleosynthesis is to occur during the late stages of supernova evolution, then the requirement of neutron-rich conditions excludes a region of neutrino mass-squared difference and vacuum mixing angle ($\delta m^2,\ \sin^22\theta$) parameter space for neutrino flavor transformation. We find that in the presence of stochastic fluctuations, this excluded region is not significantly altered even for random fluctuations with an amplitude of 1% of the local matter density.

Acoustic wave propagation in the solar atmosphere 1. Rediscussion of the linearized theory including nonstationary solutions

The normal dispersion analysis for linear adiabatic wave propagation in stratified atmospheres adopts a real frequency and solves for the complex vertical wavenumber. We show that an exponentially stratified atmosphere does not have any spatially bounded normal modes for real frequencies. The usual treatment involves a representation where the imaginary part of the vertical wavenumber yields a rho(sup -1/2) dependence of the velocity amplitude which diverges as the absolute value of z approaches infinity. This solution includes a cutoff frequency below which acoustic modes cannot propagate. The standard dispersion analysis is a local representation of the wave behavior in both space and time but which is assumed to represent the motion throughout - infinity is less than t is less than infinity and 0 is less than infinity. However, any solution which has a purely sinusoidal time dependence extends through this full domain and is divergent due to the rho(sup -1/2) dependence. We show that a proper description is in terms of a near field of a boundary piston which is driven arbitrarily as a function of space and time. The atmosphere which responds to this piston is a semi-infinite layer which has an initially constant sound speed but which has the usual gravitational stratification. In a restricted domain of space and time above this boundary, the wavelike behavior of the medium may be described by frequencies and vertical wavenumbers which are both complex. When both parameters are allowed to have imaginary components, a new range of solutions is found for which there is virtually no cutoff frequency. We show that vertical energy propagation can take place through the solar atmosphere as a result of oscillations below the nominal cutoff frequency. Previously, the largest amplitude oscillations which generally have low frequencies were dropped from the calculation of energy flux becuase their frequencies are below the cutoff frequency. This new family of near-field waves permits these modes to carry energy vertically outward and raises the possibility that the largest amplitude 5 minute oscillations play a substantial role in the transport of acoustic energy to the chromosphere.

Acoustic calibration in shallow water using sparse data

Conventional numerical techniques for calculating acoustic propagation may produce unsatisfactory results if there is insufficient information about the medium. These difficulties are exaggerated in highly variable shallow-water locales. In the proposed approach, sparse environmental measurements are supplemented by making a limited number of direct acoustic measurements. The combined data set can in principle be used to calibrate in-water systems. In this paper, acoustic calibration is demonstrated for the field extrapolation problem where the objective is to predict propagation over an extended regime. Two alternative versions of the extrapolation algorithm are first postulated and then verified analytically for the special case of adiabatic propagation. The method is then tested numerically using archival sound-speed and bathymetric data for a strongly range-dependent site. The individual and cumulative effects on down slope propagation from variations in bathymetry, imperfect knowledge of the sediment, and variability in the water column are quantified.

Fundamental limits on acoustic source range estimation performance in uncertain ocean channels

Matched-field methods which exploit complex multipath propagation models to localize underwater acoustic sources are particularly sensitive to errors in the assumed environmental parameters. In this paper, the Cramer–Rao lower bound (CRLB) is used to determine fundamental limits on the accuracy of range estimates obtained in the presence of uncertain environmental parameters. Theoretical results obtained using an adiabatic normal mode propagation model and a realistic model of sound-speed profile uncertainty indicate that without prior statistical knowledge of the environmental parameters, the CRLB may diverge even when the number of unknowns is less than the number of acoustic modes. When the prior probability distribution of the environmental parameters is available, however, the CRLB indicates a significant improvement in range estimation performance is possible. Numerical evaluation of the bound on range estimation in the presence of sound-speed profile uncertainty is performed both for an ideal waveguide and a realistic shallow-water channel using environmental data collected off the New England coast.

Wave propagation in thermoporoelastic plate

Governing equations for wave propagation of a thermoporoelastic plate are derived. The material obeys the theory of Pecker and Dersiewicz [C. Pecker and H. Dersiewicz, Acta Mech. 16, 45–64 (1973)]. The temperatures of solid and liquid phases are assumed to be different. Due to temperature difference in both phases at every point in the medium, there is a coupling parameter in heat conduction equations. The frequency equation is obtained for stress-free and thermally insulated boundary conditions. Numerical results are calculated for isothermal and adiabatic wave propagation corresponding to kerosene filled sandstone. Phase velocities and the attenuation factor are plotted against frequencies for symmetric and antisymmetric mode. In an isothermal case, the phase velocity oscillates sharply for the symmetric mode but it is not so sharp for the antisymmetric mode. But the behavior of the attenuation factor is reverse. In the adiabatic case, the phase velocity oscillates very less, up to frequency of 2 Hz; afterwards, it oscillates for both modes. In the attenuation factor, there is rapid oscillation throughout for the antisymmetric mode but it is less in the symmetric mode. Oscillation is almost absent between 2.5 and 4.5 Hz in the symmetric mode. The phase velocity is higher for the isothermal case than the adiabatic case whereas it is opposite for the attenuation factor.

Differential Doppler as a Diagnostic

Differential Doppler compression and travel time of individual peaks in the arrival sequence (relative to an overall average) are measured for the 5500-km acoustic transmissions from a moving source at Heard Island to Christmas (Crab) Island. The differentials cannot be explained by simple adiabatic propagation models. A hybrid theory, coupling polar and temperate models at the Antarctic Front, can account for some of the qualitative features. Differential Doppler could be a useful tool for identifying ray arrivals.

Wave shifts, beam shifts, and their role in modal and adiabatic propagation

On reflection from a plane interface there is a wave shift which in underwater acoustics is often called the effective depth; there is also a beam shift or beam displacement. These shifts are briefly introduced and then the relation between them is spelled out. In application to modal propagation in a range-independent medium, it is shown that a wave shift sum is invariant with respect to depth and provides an eigenvalue equation. Beam shift sums for the cycle distance and cycle time are useful but only approximately invariant, however their ratio defines the truly invariant group velocity. Propagation in a range-dependent medium is analyzed assuming the adiabatic relation; the wave shift sum is now invariant with respect to range as well. This process corresponds to a ray invariant with wave reflections at a fictitious surface defined by the wave shift. A description in terms of beam shifts is more complicated, but shown to be compatible. A simple upslope example is included.

Environmental data assimilation in matched-field processing with a random normal mode model

Numerical acoustic propagation models used in matched-field processing typically assume that ocean environmental parameters, such as the range-dependent sound-speed profile, are either known exactly or are characterized by stationary prior statistics. However, neither of these modeling approaches is well suited for accurately assimilating measurements of the correct ocean realization into the calculation of point-source acoustic wave front statistics. In this paper, environmental data is assimilated into a random adiabatic normal mode propagation model by calculating the conditional correlation matrix of an acoustic wave front given a set of contemporaneous sound-speed profile measurements made at different points in space. First-order perturbation theory is used to map the conditional statistics of Gaussian-distributed excess sound-speed variations into an estimate of the conditional point-source wave front correlation matrix. Minimum variance beamforming with environmental perturbation constraints [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1419 (1992)] conditioned on current environmental measurements is demonstrated as a means of exploiting this random wave front model to achieve improved matched-field source localization performance. [Work supported by ONR.]