Variation Of Propagation Speed Research Articles

Irregular self-similar configurations of shock-wave impingement on shear layers

An oblique shock impinging on a shear layer that separates two uniform supersonic streams, of Mach numbers $M_{1}$ and $M_{2}$, at an incident angle $\unicode[STIX]{x1D70E}_{i}$ can produce regular and irregular interactions with the interface. The region of existence of regular shock refractions with stable flow structures is delineated in the parametric space $(M_{1},M_{2},\unicode[STIX]{x1D70E}_{i})$ considering oblique-shock impingement on a supersonic vortex sheet of infinitesimal thickness. It is found that under supercritical conditions, the oblique shock fails to deflect both streams consistently and to provide balanced flow properties downstream. In this circumstance, the flow renders irregular configurations which, in the absence of characteristic length scales, exhibit self-similar pseudosteady behaviours. These cases involve shocks moving upstream at constant speed and increasing their intensity to comply with equilibrium requirements. Differences in the variation of propagation speed among the flows yield pseudosteady configurations that grow linearly with time. Supercritical conditions are described theoretically and reproduced numerically using highly resolved inviscid simulation.

TWO-DIMENSIONAL VISUALIZATION OF THE PROPAGATION SPEED OF CORTICAL SPREADING DEPRESSION IN RAT CORTEX

Cortical spreading depression (CSD), which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia, has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5 mm/min. Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique, the variation of propagation speed of CSD across different regions of cortex was not well-concerned, partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex. Here, we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex. In this method, temporal clustering analysis (TCA) and least square estimation (LSE) were first used to detect origin site where CSD was induced. Taking the origin site of CSD as the origin of coordinates, the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation. Then, two fixed-distance regions of interest (ROIs) are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm. Finally, we could draw a two-dimensional image, in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex. The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.

Numerical simulation of Lewis number effects on lean premixed turbulent flames

A dominant factor in determining the burning rate of a premixed turbulent flame is the degree to which the flame front is wrinkled by turbulence. Higher turbulent intensities lead to greater wrinkling of the flame front and an increase in the turbulent burning rate. This picture of turbulent flame dynamics must be modified, however, to accommodate the affects of variations in the local propagation speed of the flame front. Classical flame analysis characterizes these local variations in propagation speed by the Markstein number which represents the response of the flame front to curvature and strain. In this paper, we consider lean premixed flames for three different fuels having widely varying fuel Lewis numbers corresponding to widely varying Markstein numbers. In particular, we present numerical simulations of premixed turbulent flames for lean hydrogen, propane and methane mixtures in two dimensions. Each simulation is performed at turbulence conditions similar to those found in laboratory-scale experiments and is performed using detailed chemical kinetics and transport properties. We discuss the effect of Lewis number on the overall flame morphology and explore the dependence of local flame propagation speed on flame curvature. We also explore the relationship between local flame speed and experimentally accessible variables such as OH concentration. Finally, we focus on the low Lewis number case, hydrogen, in which the flame front is broken indicating local extinction.

The Effects of Photon Bubble Instability in Radiation‐dominated Accretion Disks

We examine the effects of photon bubble instability in radiation-dominated accretion disks such as those found around black holes in active galactic nuclei and X-ray binary star systems. Two- and three-dimensional numerical radiation MHD calculations of small patches of disk are used. Modes with wavelengths shorter than the gas pressure scale height grow faster than the orbital frequency in the disk surface layers. The fastest growth rate observed is 5 times the orbital frequency and occurs on nearly vertical magnetic fields. The spectrum of linear modes is in good agreement with a WKB analysis that indicates still faster growth at unresolved scales, with a maximum growth rate proportional to the gravitational acceleration and inversely proportional to the gas sound speed. Disturbances reaching nonlinear amplitudes steepen into trains of shocks similar to a one-dimensional periodic nonlinear analytic solution. Variations in propagation speed result in merging of adjacent fronts, and over time the shock spacing and amplitude increase. Growth is limited by the strength of the magnetic field. The shock train structure is disrupted when the ram pressure of the disturbances exceeds the magnetic pressure. The maximum horizontal density variations are comparable to the ratio of magnetic to gas pressure and in our calculations exceed 100. Under the conditions considered, radiation diffuses through the inhomogeneneous flow 5 times faster than through the initial hydrostatic equilibrium, and the net cooling rate is several times greater than in a similar calculation without magnetic fields that shows the effects of convection. These results indicate that photon bubbles may be important in cooling radiation-dominated accretion disks. The Shaviv type I global instability grows faster than the orbital frequency in calculations of the disk surface layers with lower boundaries of fixed temperature, but is weak or absent in calculations spanning the disk thickness.

Bounding the mass of the graviton using gravitational-wave observations of inspiralling compact binaries

If gravitation is propagated by a massive field, then the velocity of gravitational waves (gravitons) will depend upon their frequency and the effective Newtonian potential will have a Yukawa form. In the case of inspiralling compact binaries, gravitational waves emitted at low frequency early in the inspiral will travel slightly slower than those emitted at high frequency later, modifying the phase evolution of the observed inspiral gravitational waveform, similar to that caused by post-Newtonian corrections to quadrupole phasing. Matched filtering of the waveforms can bound such frequency-dependent variations in propagation speed, and thereby bound the graviton mass. The bound depends on the mass of the source and on noise characteristics of the detector, but is independent of the distance to the source, except for weak cosmological redshift effects. For observations of stellar-mass compact inspiral using ground-based interferometers of the LIGO/VIRGO type, the bound on the graviton Compton wavelength is of the order of $6 \times 10^{12}$ km, about double that from solar-system tests of Yukawa modifications of Newtonian gravity. For observations of super-massive black hole binary inspiral at cosmological distances using the proposed laser interferometer space antenna (LISA), the bound can be as large as $6 \times 10^{16}$ km. This is three orders of magnitude weaker than model-dependent bounds from galactic cluster dynamics.

Propagation of a Tropical Cyclone in a Meridionally Varying Zonal Flow: An Energetics Analysis

Abstract Tropical cyclone propagation (the beta drift) is driven by a secondary circulation associated with axially asymmetric gyres (beta gyres) in the vicinity of the cyclone center. In the presence of the beta effect, the environmental flow may interact with the symmetric circulation and beta gyres of the cyclone, affecting the development of the gyres and thereby the cyclone propagation. An energetics analysis is carried out to elucidate the development mechanism of the beta gyres and to explain variations in propagation speed of a barotropic cyclone embedded in a meridionally varying zonal flow on a beta plane. Two types of zonal flows are considered: one with a constant meridional shear resembling those in the vicinity of a subtropical ridge or a monsoon trough, and the other with a constant relative vorticity gradient as in the vicinity of an easterly (westerly) jet. Zonal flow with a constant meridional shear changes the generation rate of the gyre kinetic energy through an exchange of energy dire...

Simple theory of the effects of medium turbulence upon scanning with an adaptive phased array

Medium turbulence, characterized by local variations in propagation speed, limits array size to the order of the correlation distance of the velocity perturbation. Array gain is lost when the array size significantly exceeds that distance. Adaptive beamforming eliminates this size constraint on the array. However, the scanning distance then turns out to be limited, the amount being proportional to the correlation distance and the proportionality constant being a function of the scanning direction. The size and shape of the scanning sector is calculated, along with the number of resolution cells that it contains, both for passive and active sonar systems.

The magnetic‐anomaly model of the Jovian magnetosphere: A post‐Voyager assessment

We reexamine the three predictions that we previously put forth as tests for the magnetic‐anomaly model (in which the anomalously weak magnetic field region in the northern hemisphere of Jupiter influences the outer Jovian magnetosphere by one or more plasma interaction processes), taking into account the Voyager and other recent observations. Concerning the prediction of a restricted longitude range of enhanced interaction between Io and Jupiter's ionosphere, the longitudinal asymmetries seen in ground‐based observations of sulfur emissions from the Io torus as well as in Voyager observations of Jovian auroral emissions agree with the predicted asymmetries. The lowered estimates of the Alfvén speed in the Io torus as a result of Voyager composition determinations modify many earlier ideas on the magnetosphere/Io interaction, but the conclusion remains that longitudinal asymmetries with a 360° period can be plausibly explained only by reference to magnetic‐anomaly effects. Concerning the predictions of plasma, energetic particle, and magnetic field periodicities in the outer magnetosphere being related to either a current sheet or a magnetic‐anomaly effect, we conclude that the hitherto common interpretation of Voyager observations in terms of a current sheet with no longitudinal asymmetries is seriously deficient because a bending of the current sheet from 40 to 60 RJ outward is required whereas the Pioneer 10 observations demand that there be no such bending; attempts to reconcile Voyager and Pioneer by invoking time variations or solar wind effects are inconsistent with the observed constancy of propagation speeds for configurational changes and with the observed ratio of magnetic pressure to solar wind pressure. We construct a simple quantitative model with a sinusoidal longitudinal variation of inverse speed and show that the inclusion of such a variation of propagation speed (as implied by the magnetic‐anomaly model) into the description of the current sheet removes these inconsistencies and allows a unified interpretation of both Voyager and Pioneer observations. Concerning the prediction of a longitudinally restricted distribution of magnetopause crossings, the evidence for a clustering of magnetopause crossings near the active sector remains suggestive but statistically inconclusive. These results, combined with a number of other observed phenomena that cannot be accounted for by a pure magnetodisc model with no longitudinal asymmetries, provide evidence that magnetic‐anomaly effects play a significant role in determining the behavior of the Jovian magnetosphere.

One‐dimensional velocity inversion for acoustic waves: Numerical results

We consider the inverse problem of determining small variations in propagation speed from remote observations of signals which pass through an inhomogeneous medium. Under the conditions (1) that the variations can be written as a small perturbation from a known reference value and (2) that the medium of interest varies in one direction only, an integral equation has been developed for the variations which can be solved in closed form. Here, a technique is presented to obtain and process synthetic data from a scattering profile of arbitrary shape. The results of numerical testing show that, as long as a velocity variation is indeed ’’small,’’ both its size and its shape can be reproduced with negligible error by this method.

An Inverse Method for Determining Small Variations in Propagation Speed

We consider the inverse problem of determining small variations in propagation speed from observations of signals which pass through the medium of interest and are then observed remotely. We show that the variation satisfies an integral equation of integral transform type with an atypical kernel. In a variety of examples for the scalar and vector wave equation (Maxwell’s equations) and the equations of linear elasticity, we solve this integral equation by elementary means.

Gradual Reflection of Short Waves

Short wave asymptotic methods (geometrical optics, WKB, averaging and two-timing, etc.) fail to give information on the wave reflection caused by gradual variation of propagation speed with position. This paper examines plane wave propagation according to the classical wave equation in a medium of optical index of refraction changing analytically smoothly in the direction of propagation. The reflection coefficient is shown to be exponentially small in the ratio of wavelength to modulation scale. It is calculated to the first approximation for a large class of analytical index functions.

Global atmospheric pressure effects of the October 30, 1961, explosion

The atmospheric pressure waves set off by the explosion of October 30, 1961, were traced over a large portion of the world, including the antipodes in the Antarctic, by means of analyses of available ordinary microbarograph records. The observed geographic variations in propagation speed and maximum amplitude are examined with the aid of air density and wind analyses. Comparison is made with the waves resulting from the great Siberian meteor of 1908 and the Krakatoa eruption of 1883.