Amplitude Of Velocity Perturbations Research Articles

Analysis on Thermo-Electrical Principal Parametric Resonance of an Axially Moving Piezoelectric Thin Plate

In this paper, principal parametric resonance of an axially moving piezoelectric rectangular thin plate under thermal and electric field is investigated. Based on Kirchhoff–Love plate theory and Von Karman theory, the transverse vibration differential equation of a piezoelectric rectangular thin plate under thermal and electric field is derived by using Hamilton’s principle. The dimensionless vibration equation of piezoelectric rectangular thin plate with parametric excitations is discretized by Galerkin’s method. Then, the multiple scales method is applied to derive amplitude-frequency response equation and the stability conditions of the steady-state solution are obtained by Lyapunov stability theory. Numerical method is used to find the influences of specific parameters on the vibration performance and stability of the system. Based on the global bifurcation diagram and corresponding response diagram, the influences of bifurcation control parameters on the nonlinear dynamic characteristics of the system are discussed. Numerical results illustrate that the system amplitude frequency characteristic curve presents soft spring characteristics. There are periodic and chaotic motions with the increase of velocity and the central temperature difference, and the decrease of plate thickness and velocity will result in the decrease of chaotic threshold. The results also show that increase the velocity perturbation amplitude can prolong the chaotic motion.

Generation of the small tin-droplet streams with a manipulable droplet spacing via the forced velocity perturbation

In extreme ultraviolet (EUV) sources, small tin droplets are scattered into the tin mist/disk under the irradiation of the pulsed laser to produce the EUV light. Small droplet size and large droplet spacing are required to suppress debris production to protect expensive collector mirrors. To this end, a tin-droplet generator with a capillary glass nozzle was designed and built to produce uniform tin-droplet streams with the droplet diameter less than 50 μm. Meanwhile, a forced perturbation, generated by a sandwich piezoelectric transducer, was loaded into a liquid tin jet to manipulate the droplet spacing through a stepped rod. The mono-sized tin-droplet streams with an average diameter of 42 μm were successfully produced in both the Rayleigh and the forced jet breakup regimes. A two-dimensional (2D) axisymmetric model was proposed to reveal the influence of the velocity perturbation amplitude on jet breakup patterns at different wavelengths. An F*–λ* (The dimensionless perturbation velocity amplitude F*–The dimensionless wavenumber l*) map was built, and five different droplet breakup patterns were identified based on simulations. Numerical simulations indicated that the droplet spacing could be increased by providing extra momentum to droplets from the forced velocity perturbation. Finally, by increasing the velocity perturbation amplitude, the droplet spacing was increased from ∼9Dd (droplet diameter) to ∼19Dd without significantly increasing the droplet size. This work provides a novel approach to obtaining small mono-sized tin-droplet streams with manipulable droplet spacing.

Parameters of the Radcliffe Wave from Masers, Radio Stars, and T Tauri Stars

The presence of the Radcliffe wave is shown both in the positions and in the vertical velocities of masers and radio stars belonging to the Local Arm. This gives the impression that the structure of the Radcliffe wave is not a wave in the full sense of the word. It is more like a local high-amplitude burst, rapidly fading away. Moreover, this structure has the largest amplitude in the immediate vicinity of the Sun, where the main ``contributors'' are the Gould Belt stars. Based on the spectral analysis of masers, the following estimates of the geometric and kinematic characteristics of the wave were obtained: the largest value of the vertical coordinate $z_{max}=87\pm4$ pc and the wavelength $\lambda=2.8\pm0.1$ kpc, the vertical velocity perturbation amplitude reaches $W_{max}=5.1\pm0.7$ km s$^{-1}$ and the wavelength found from vertical velocities is $\lambda=3.9\pm1.6$ kpc. The Radcliffe wave also manifests itself in the positions of very young stars that have not reached the main sequence stage. We extracted a sample of such stars from the Gaia DR2$\times$AllWISE database and obtained the following estimates from them: $z_{max}=118\pm3$ pc and wavelength $\lambda=2.0\pm0.1$ kpc.

Parameters of the Galactic Spiral Density Wave from Masers with Parallax Errors Less Than 10$$\boldsymbol{\%}$$

We have studied the kinematics of Galactic masers and radio stars with measured VLBI trigonometric parallaxes and proper motions. We have considered masers with relative trigonometric parallax errors less than 10\% and determined the Galactic rotation parameters from them. In particular, the linear rotation velocity of the Galaxy at the solar distance $R_0$ has been found to be $244.4\pm4.3$ km s$^{-1}$ (for the adopted $R_0=8.1\pm0.1$ kpc). We have performed a joint and separate spectral analysis of the radial, residual tangential, and vertical maser velocities. For example, from the vertical maser velocities we have estimated the velocity perturbation amplitude $f_W=5.2\pm1.5$ km s$^{-1}$ with the wavelength $\lambda_W=2.6\pm0.7$ kpc, arguing for the influence of the spiral density wave on the vertical stellar velocities. Based on 104 masers within 3 kpc of the Sun, as a result of the joint solution, we have estimated the radial, $f_R=6.7\pm1.1$ km s$^{-1}$, and tangential, $f_\theta=2.6\pm1.2$ km s$^{-1}$, velocity perturbations, the perturbation wavelength $\lambda=2.1\pm0.3$ kpc, and the Sun's phase in the Galactic spiral density wave $\chi_\odot=-148\pm15^\circ$. We have confirmed the presence of the Radcliffe wave in the spatial distribution of masers and radio stars belonging to the Local Arm.

Generation of the Vortex Movement in the Atmosphere due to Gravity Inhomogeneities

One possible mechanism for the effect of gravity-field inhomogeneities (GFIs) on the atmosphere dynamics has been investigated theoretically. It is shown that the vertical heat exchange in an air layer in an inhomogeneous gravity field can disrupt the state of hydrostatic equilibrium and lead to the generation of vortex flows. Estimates of the amplitude of velocity perturbations are made on the basis of a linear stationary hydrodynamic model that takes planetary rotation into account. The magnitude of the vortex component of the velocity can reach values on the order of the product of the buoyancy frequency and amplitude of the geoid deviations. The amplitude of the emerging vertical motions, in addition to the parameters mentioned, also depends on the intensity of the turbulent exchange and horizontal scales of the inhomogeneities.

Generation of Shear Motion from an Isotropic Explosion Source by Scattering in Heterogeneous Media

One challenging task in explosion seismology is the development of physical models for explaining the generation of S waves during underground explosions. Recent analysis of ground motion from chemical explosions during the Source Physics Experiment (Pitarka et al. , 2015) suggests that, although a large component of shear motion was generated directly at the source, additional scattering from heterogeneous velocity structure and topography is necessary to better match the recorded data. In our study, we used a stochastic representation of small‐scale velocity variability to produce high‐frequency scattering and to analyze its implication on shear‐motion generation during underground explosions. In our stochastic velocity model, the key parameters that affect scattering are the correlation length and the relative amplitude of velocity perturbations. Based on finite‐difference simulations of elastic wave propagation from an isotropic explosion source, we find that higher velocity perturbations result in larger shear motion, whereas the correlation length, which controls the scatterers size, affects the frequency range at which relative transverse motion is larger.

Prominence oscillations: Effect of a time-dependent background temperature

Context. Small amplitude oscillations in prominences have been known about for a long time, and from a theoretical point of view, these oscillations have been interpreted in terms of standing or propagating linear magnetohydrodynamic (MHD) waves. In general, these oscillations were studied by producing small perturbations in a background equilibrium with stationary physical properties. Aims. Taking into account that prominences are dynamic plasma structures, the assumption of a stationary equilibrium is not realistic. Therefore, our main aim is to study the effects produced by a non-stationary background on slow MHD waves, which could be responsible for prominence oscillations. Methods. Assuming that the radiation term is proportional to temperature and constant external heating, we have derived an expression for the temporal variation of the background temperature, which depends on the imbalance between heating and cooling processes. Furthermore, radiative losses, together with parallel thermal conduction, have also been included as damping mechanisms for the waves. Results. As temperature increases with time, the period of slow waves decreases and the amplitude of the velocity perturbations is damped. The inclusion of radiative losses enhances the damping. As temperature decreases with time, the period of slow waves increases and the amplitude of velocity perturbations grows while, as expected, the inclusion of radiative losses contributes to the damping of oscillations. Conclusions. There is observational evidence that, in different locations of the same prominence, oscillations are damped or amplified with time. This temporal damping or amplification can be obtained by a proper combination of a variable background temperature, together with radiative damping. Furthermore, decayless oscillations can also be obtained with an appropriate choice of the characteristic radiation time.

Propagation and damping of slow MHD waves in a flowing viscous coronal plasma

We investigate the propagation of slow MHD waves in a flowing viscous solar coronal plasma. The compressive viscosity and steady flow along and opposite to the wave propagation are taken into account to study the damping of slow waves. We numerically solve the MHD equations by MacCormack method to examine the effect of steady flow on the damping of slow MHD waves in viscous solar coronal plasma. Amplitude of velocity perturbation and damping time of slow waves decrease with the increase in the value of Mach number. Flow causes a phase shift in the perturbed velocity amplitude and an increase in wave period. The damping of slow waves in flowing viscous plasma is stronger than the damping of waves in viscous plasma. Slow wave in backward flow damps earlier than the wave in forward flow.

FORWARD MODELING OF STANDING SLOW MODES IN FLARING CORONAL LOOPS

Standing slow mode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Due to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slow mode waves in flaring loops and compare the synthesized line emission properties with SUMER spectrographic and SDO/AIA imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity both in time and spatial domain, which can be used to identify a standing slow mode wave from spectroscopic observations. However, the longitudinal overtones could be only measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations, this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect \textbf{half} periodicity close to the loop apex, where emission intensity modulation is relatively small. The line-of-sight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by de-projecting the Doppler shift by a factor of $1-2\theta/\pi$ rather than the traditionally used $\cos\theta$. \textbf{If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.

Analytical estimate of phase mixing time of longitudinal Akhiezer-Polovin waves

Phase mixing of a longitudinal Akhiezer-Polovin wave subjected to a small amplitude longitudinal perturbation and its eventual breaking is studied analytically. It is well known that longitudinal Akhiezer-Polovin wave subjected to arbitrarily small longitudinal perturbation breaks via the process of phase mixing at an amplitude well below its limiting amplitude [Verma et al., Phys. Rev. Lett. 108, 125005 (2012)]. We analytically show that the phase mixing time (breaking time, ωpτmix) scales with β (phase velocity) and um(maximum fluid velocity) as ωpτmix∼2πβ3δ[1/um2−1/4], where δ is the amplitude of velocity perturbation and ωp is the non-relativistic plasma frequency. This analytical dependence of phase mixing time on β, um, and δ is further verified using numerical simulations based on Dawson sheet model.

Parametric survey of longitudinal prominence oscillation simulations

It is found that both microflare-sized impulsive heating at one leg of the loop and a suddenly imposed velocity perturbation can propel the prominence to oscillate along the magnetic dip. An extensive parameter survey results in a scaling law, showing that the period of the oscillation, which weakly depends on the length and height of the prominence, and the amplitude of the perturbations, scales with $\sqrt{R/g_\odot}$, where $R$ represents the curvature radius of the dip, and $g_\odot$ is the gravitational acceleration of the Sun. This is consistent with the linear theory of a pendulum, which implies that the field-aligned component of gravity is the main restoring force for the prominence longitudinal oscillations, as confirmed by the force analysis. However, the gas pressure gradient becomes non-negligible for short prominences. The oscillation damps with time in the presence of non-adiabatic processes. Compared to heat conduction, the radiative cooling is the dominant factor leading to the damping. A scaling law for the damping timescale is derived, i.e., $\tau\sim l^{1.63} D^{0.66}w^{-1.21}v_{0}^{-0.30}$, showing strong dependence on the prominence length $l$, the geometry of the magnetic dip (characterized by the depth $D$ and the width $w$), and the velocity perturbation amplitude $v_0$. The larger the amplitude, the faster the oscillation damps. It is also found that mass drainage significantly reduces the damping timescale when the perturbation is too strong.

Non-linear Response of Turbulent Premixed Flames to Imposed Inlet Velocity Oscillations of Two Frequencies

This paper describes an experimental study investigating the non-linear response of lean premixed air/ethylene flames to strong inlet velocity perturbations of two frequencies. The combustor has a centrally-placed bluff body and a short quartz section. The annulus between the bluff body and the flow tube, which also housed the acoustic pressure transducers, allowed the reactants into the combustor. The inlet flow was perturbed using loudspeakers. High speed laser tomography, OH* chemiluminescence and OH Planar Laser Induced Fluorescence (PLIF) have been used for flow visualization, heat release and flame surface density (FSD) measurements respectively. The heat release fluctuations increased initially linearly with inlet velocity amplitude for a single frequency forcing, with saturation occurring after forcing amplitudes of around 15% of the bulk velocity, which was found to occur due to vortex roll up and subsequent flame annihilation. The introduction of energy at the second frequency (i.e, the harmonic) was found to change the vortex formation and shedding frequency, depending on the level of forcing. This resulted in a non-linear flame response transfer function (defined as the amplitude of unsteady heat release divided by the amplitude of velocity perturbation at the fundamental) whose amplitude depended greatly on the amount of harmonic content present in the perturbations. The introduction of higher harmonics reduced the flame annihilation events, which are responsible for saturation, thus reducing non-linearity in the amplitude dependence of the flame response. These results were further verified using sequential time-resolved OH PLIF measurements. The findings from this study suggest that the acoustic response of the flame was mostly due to flame area variation effected by modulation of the annular jet and evolution of the shear layers.

Combustion dynamics of inverted conical flames

An inverted conical flame anchored on a central bluff-body in an unconfined burner configuration features a distinctive acoustic response. This configuration typifies more complex situations in which the thermo-acoustic instability is driven by the interaction of a flame with a convective vorticity mode. The axisymmetric geometry investigated in this article features a shear region between the reactive jet and the surrounding atmosphere. It exhibits self-sustained oscillations for certain operating conditions involving a powerful flame collapse phenomenon with sudden annihilation of flame surface area. This is caused by a strong interaction between the flame and vortices created in the outer jet shear layer, a process which determines the amplitude of heat release fluctuation and its time delay with respect to incident velocity perturbations. This process also generates an acoustic field that excites the burner and synchronizes the vortex shedding mechanism. The transfer functions between the velocity signal at the burner outlet and heat release are obtained experimentally for a set of flow velocities fluctuations levels. It is found that heat release fluctuations are a strong function of the incoming velocity perturbation amplitude and that the time delay between these two quantities is mainly determined by the convection of the large scale vortices formed in the jet shear layer. A model is formulated, which suitably describes the observed instabilities.

Weakly nonlinear subcritical instability of visco-elastic Poiseuille flow

It is well known that the Poiseuille flow of a visco-elastic polymer fluid between plates or through a tube is linearly stable in the zero Reynolds number limit, although the stability is weak for large Weissenberg numbers ( Wi ). In this paper, we argue that recent experimental and theoretical work on the instability of visco-elastic fluids in Taylor–Couette cells and numerical work on channel flows suggest a scenario in which Poiseuille flow of visco-elastic polymer fluids exhibits a nonlinear “subcritical” instability due to normal stress effects, with a threshold which decreases for increasing Weissenberg number. This proposal is confirmed by an explicit weakly nonlinear stability analysis for Poiseuille flow of an UCM fluid. Our analysis yields explicit predictions for the critical amplitude of velocity perturbations beyond which the flow is nonlinearly unstable, and for the wavelength of the mode whose critical amplitude is smallest. The nonlinear instability sets in quite abruptly at Weissenberg numbers around 4 in the planar case and about 5.2 in the cylindrical case, so that for Weissenberg numbers somewhat larger than these values perturbations of the order of a few percentage in the wall shear stress suffice to make the flow unstable. We have suggested elsewhere that this nonlinear instability could be an important intrinsic route to melt fracture and that preliminary experiments are both qualitatively and quantitatively in good agreement with these predictions.

Mixing of Young Neutron Star Debris Into Supernova Envelopes

We have simulated the 3D growth of a Rayleigh-Taylor instability in the expanding envelope of SN 1987A using the Adaptive Mesh Refinement Scheme utilizing a resolution of 4096−3. When the sinusoidal velocity perturbation amplitude is 10%, heavy element tongues of the He/H interface penetrate into the envelope with a high velocity.

TheS-velocity structure of the East Asian mantle from inversion of shear and surface waveforms

SUMMARY The structure of the mantle beneath East Asia down to 800 km depth is investigated using full waveforms of seismic shear and surface waves. Epicentral distances are limited to less than 40°. In contrast with previous waveform inversions, we avoid ray-theoretical or path-integral approaches. Instead, we use (1) exact 3-D waveform sensitivity kernels that correctly reflect off-path sensitivity and the existence of Fresnel zones. We apply (2) an accurate 3-D forward modelling technique based on a coupled-mode, multiple-forward-scattering approach, allowing us (3) to iterate the inversion procedure through several 3-D models and (4) to evaluate the true misfit between the data and the synthetics for the 3-D model. Average lateral resolution of the model in regions with good path coverage is 400 km throughout the upper mantle. In the depth range from 100 to 250 km the lateral resolution even approaches 200 km. Since wave front healing is taken into account, the amplitudes of velocity perturbations are larger than in other tomographic models. Moreover, the waveform sensitivity kernels provide an intrinsic physical smoothing of the model, stabilizing the inversion. Finally, owing to the use of exact sensitivities, better resolution can be achieved with a given set of seismograms. Major features of the model are high-velocity subducting slabs along the West Pacific subduction zones stagnating at the 660 km discontinuity, a strong low-velocity zone between 80 and 250 km depth in the West Pacific backarc regions, a plume-like low-velocity feature beneath the southern tip of the Baikal rift zone extending into the transition zone, a low-velocity region under the Tien Shan with connection into the transition zone and thick crust under Tibet reaching its maximum thickness of approximately 80 km close to the 35th parallel. The lithospheric mantle underneath southern Tibet is very fast indicating underthrusting of the Indian lithosphere. In contrast, the upper mantle beneath northern Tibet exhibits average-to-slow values from the Moho down to the 660 km discontinuity. Very high S velocities are again observed beneath the Tarim Basin. The high-velocity mantle lithospheres under southern Tibet and the Tarim join beneath the Karakorum range at the western tip of the Tibet Plateau.

Tomographic imaging of the lowermost mantle with differential times of refracted and diffracted core phases (PKP, Pdiff)

The mapping of variations in P wave speed in the deep mantle is restricted by the uneven sampling of P waves, in particular beneath the Southern Hemisphere. To enhance data coverage, we augmented the ∼1.6 million summary rays of P, pP, and pwP that we used in previous studies with differential travel times of diffracted and refracted core phases. For the core‐refracted differential travel time residuals (PKPAB‐PKPDF and PKPAB‐PKPBC) we used 1383 cross‐correlated digital waveforms as well as ∼27,000 routinely processed bulletin data. We used the waveform data to define quality criteria for the selection and reduction of the bulletin PKP data. For PKPDF‐Pdiff we only considered 543 records derived from waveform cross correlation. No PcP data were used in this study. We used optical ray theory to calculate the ray paths associated with the P, pP, pwP, and PKP data, which are measured at 1 Hz. However, to account for the large Fresnel zones of the low‐frequency (∼50 mHz) PKPDF‐Pdiff data we estimated the three‐dimensional shape of the Fréchet sensitivity kernels from kernels calculated by normal mode summation. The use of these kernels allows us to properly distribute the sensitivity for a given seismic phase over a large mantle volume while allowing the high‐frequency data to constrain small‐scale structure. The differential times are relatively insensitive to source mislocation and to structure in the shallow mantle beneath source and receivers, and they have previously been interpreted exclusively in terms of lateral structure directly above the core mantle boundary (CMB). However, images thus obtained can be contaminated by effects of small scale structure elsewhere in the mantle. Here, we do not make a priori assumptions about the mantle source of anomalous time differentials. From test inversions we conclude that (both upper and lower) mantle structures that are poorly resolved by P data can be mapped into the core along PKP paths but that the effect of outer core structures, if any, on the mantle model is small. Compared to the inversion of the P, pP, and pwP alone, the inclusion of the PKPAB‐PKPDF and PKPAB‐PKPBC and PKPDF‐Pdiff data improves the resolution of structure beneath 2200 km depth. In particular, the joint inversion puts better constraints on the long‐wavelength variations in the very deep mantle and yields an increase in the amplitude of velocity perturbations near the CMB that is in agreement with but still smaller than inferences from shear wave studies. Resolution tests indicate that in some regions the enhanced definition of structure is significant, but in most regions the improvements are subtle and structure remains poorly resolved in large regions of the mantle.

High-order azimuthal instabilities on a cylindrical liquid jet driven by temporal and spatial perturbations

A method has been developed to drive a cylindrical liquid jet unstable for deformations with axial wavelengths shorter than the circumference of the jet and azimuthal mode numbers greater than 0. The benefit of this method is that a cylindrical liquid jet can be broken into a spray with an average diameter smaller than the diameter of the initial jet. The higher-order instabilities were created by establishing initial conditions for the jet in space and time at the nozzle. An electromechanical transducer creates the applied temporal initial condition which is a sinusoidally varying velocity perturbation added to the steady velocity of the jet. The amplitude of the velocity perturbation can be as large as the jet’s steady velocity and the energy in the applied velocity perturbation drives the instability. The spatial perturbation is created by placing perturbations in the circumference of the nozzle. As the velocity perturbation travels on the jet, its leading edge steepens and the trailing edge broadens in a manner analogous to the steepening of a pressure pulse in a compressible gas. If the driven velocity perturbation is sufficiently large, a shock or jump forms on the leading edge of the velocity pulse and the jet may break up into higher-order modes. A theoretical analysis of the breakup process, based on an adaptation of compressible fluid shock theory, is used to derive a fundamental lower bound on the spray’s Sauter mean diameter as a function of the velocity perturbation amplitude. Techniques for approaching the theoretical minimum spray diameter by using the higher-order modes to atomize liquid jets are discussed.

Localization of combustion in a periodic velocity field

A direct numerical simulation of combustion-front propagation in a specified periodic velocity field of a medium was performed within the framework of a two-dimensional thermal diffusion formulation. The calculations showed that as the velocity amplitude is increased, the flame front separates into discrete burning segments, i.e., spatial localization of the combustion takes place. Only when heat losses are introduced into the model, flame quenching is observed at a certain amplitude of the medium’s velocity. The level of heat losses required to extinguish the combustion becomes lower with increase in the amplitude of velocity perturbations. On the whole, the obtained numerical results agree with results of an asymptotic analysis.

Tomographic studies of the upper mantle beneath the Italian region*

ABSTRACTTeleseismic P arrivals at seismological stations are inverted into a model of velocity perturbations down to a depth of about 470 km. Directionally independent average residuals, computed from steeply inciding waves, are transformed into a model of lithospheric thickness. Both models show a good correspondence with the main tectonic features of the Italian Peninsula. Positive velocity perturbations are observed beneath the Alps and in depths over 200 km also beneath the Po Basin. A high‐velocity anomaly of the Tyrrhenian subduction is less pronounced, probably due to a directional dependence of P velocities in the mantle. Negative velocity perturbations indicate several low‐velocity regions, e.g. beneath the Northern Apennines, the Sicily region and in the upper 100 km beneath the Po Basin. The amplitudes of velocity perturbations beneath the depth of 200 km are smaller on the average than those in the upper two layers. The whole region is characterized by large undulations of the lithosphere base which reaches depths from less than 60 km to more than 150 km. The most prominent lithospheric root beneath the Alps is a product of the collision between the European and the Adriatic plates while the lithospheric thickening beneath the Calabrian coast is likely to be connected with the eastern wing of the Tyrrhenian subduction. The dramatic changes of lithosphere thickness between the northern and the southern Apenninic arcs and northern Calabria as well as the thinnings at the western closure of the Po Basin, indicate important deep‐seated boundaries of lithospheric blocks of autonomous geodynamic development.