Unstable Velocity Distribution Research Articles

Linear stability of mixed convection in a differentially heated vertical channel filled with high permeable porous-medium

Linear stability analysis is used to analyze the stability of parallel flow induced by an external pressure gradient and buoyancy force in a differentially heated vertical channel filled with a fluid-saturated high permeable porous medium. The non-Darcy model which gives rise to the volume averaged Navier-Stokes (VANS) equation is used except for some comparative study where Darcy model is also used. The investigation is made for a wide range of Prandtl numbers (Pr) that includes mercury, air, water and heavy oils. The spectral method has been adopted to solve the governing equations of the problem. In the entire considered range of Reynolds number (Re) the linear stability results show that the type of instability for mercury is thermal-shear (i.e., the instability is hydrodynamic in origin, resulting from an unstable velocity distribution, and obtains most of its kinetic energy (KE) through shear source), for water as well as heavy oil it is thermal-buoyant (i.e., most of the KE for this instability is obtained through work done by fluctuating buoyant force), whereas for air it is interactive (i.e., KE for this instability is obtained from both shear as well as buoyant sources). When Re is fixed at 1000, the appearance of point of inflection in the basic flow velocity for a fluid with Pr less than 30 acts as a necessary condition for instability for all considered values of Darcy number. Furthermore, the form drag stabilizes the fluid flow with Pr≥7, however, it acts other way up to a threshold value for fluid flow with Pr<1. Finally, scale analysis reveals that for thermal-shear or interactive instability the minimum critical ΔT for parallel mixed convection flow is less than the same for parallel natural convective flow and it is other way for thermal-buoyant instability. As an example of thermal-buoyant instability, when the channel is filled with a porous medium having permeability 2.5 ×10−6m2 and half-width 5 cm, the mixed convective flow of water remains stable up to a temperature difference of 13.3oC between the walls, whereas the natural convective flow of water remains stable up to a temperature difference of 8.58oC between the walls.

Evaluation of Burden Descent Model for Burden Distribution in Blast Furnace

Mathematical models for burden descending process have been applied to obtain whole burden structures in blast furnace, whereas the accuracy of those burden descent models has not been sufficiently investigated. Special evaluation method based on timeline burden profiles was established to quantitatively evaluate the error between experimental and modeled burden structures. Four existing burden descent models were utilized to describe the burden structure of a 1/20 sealed warm blast furnace. Input modeling conditions including initial burden profile, descending volumes in each time interval, and normalized descending velocity distribution were determined via special image processing technology. Modeled burden structures were evaluated combined with the published experimental data. It is found that all the models caught the main profile of the burden structure. Furthermore, the improved nonuniform descent model (Model IV) shows the highest level of precision especially when burden descends with unstable velocity distribution tendency. Meanwhile, the traditional nonuniform descent model (Model III) may also be desirable to model the burden descending process when the burden descending velocity presents a linear tendency. Finally, the uniform descent model (Model I) might be the first option for roughly predicting burden structure.

PLASMA DYNAMICS AT THE PROMINENCE-CORONA INTERFACE

The interface between the cool and dense plasma typical of a prominence and its tenuous and hot surrounding coronal plasma is poorly understood. We study the plasma dynamics at this interface using a three-dimensional particle-in-cell code, which enables us to carry out simulations on spatial and temporal scales of the order of the Debye length and plasma period, respectively. The results show that anomalous Bohm diffusion across magnetic field lines occurs at the interface, leading to mixing of the two plasmas. It is also shown that collisions with neutral hydrogen within the prominence plasma are of little importance for the plasma dynamics in the prominence-corona transition region. In particular, the temperature of the prominence plasma crossing the interface into the corona can become anisotropic due to preferential heating by instabilities originating from unstable velocity distributions. Our results pertain to spatial scales significantly smaller than scales commonly used in magnetohydrodynamic simulations, and they shed light on processes that are very likely to be present at the interface.

Direct and indirect generation of Jovian quasiperiodic radio bursts by relativistic electron beams in the polar magnetosphere

[1] The Jovian polar magnetosphere has relativistic particle accelerations with quasiperiodicity (QP accelerations), which are accompanied by periodic auroral emissions and low-frequency radio bursts called QP bursts. Although there have been some observations, the generation process of QP bursts by relativistic electrons from QP accelerations has not been revealed yet. This paper presents calculated wave growth rates for the discussion of the QP radio burst generation processes based on wave generation theories. Linear growth rates were computed for free space mode waves and plasma waves in cold plasma dispersion relations, assuming that these waves are generated by relativistic electron beams in two kinds of polar source regions, as suggested by wave observations and by the ray-tracing results reported in our previous studies. One of the source regions is at high altitudes where emission frequency f is close to local right-handed extraordinary (RX) mode cutoff frequency fRX and the other is at low altitudes where f is close to local plasma frequency fp. We found that ordinary (O) mode free space waves are sufficiently amplified, with broad beaming at both of the sources in the duration of the relativistic electron populations when they have an unstable velocity distribution like a ring beam structure. This means that O mode free space waves can be generated directly from energetic electrons via the “cyclotron maser instability” (CMI) process. We also confirmed that extraordinary (X) mode free space waves are not sufficiently amplified at both of the sources in the beam duration but Z mode waves propagating along field lines from the sources toward the Jovian polar ionosphere are significantly excited. Z mode waves propagating toward the planet could be converted to free space O mode waves at a steep plasma density gradient via the “mode conversion” (MC) process. We conclude that both direct (CMI) and indirect (MC) process can generate O mode QP radio bursts with radiation characteristics consistent with those observed by spacecraft. This suggests that relativistic electrons with unstable velocity distributions are generated by the QP acceleration and that Z mode and O mode QP radio bursts are excited by these particles.

射出成形機のホッパー下における樹脂ペレット噛込み状況の可視化解析 Ｉ 噛込み不良現象の解析

Stable pellet-conveyance around the feed throat of the heating cylinder of an injection molding machine is an especially important element in precision molding. In this study, we observed the pellet-conveying behavior of several resins using simultaneous visualization equipment for both the feed throat area and the heating cylinder in order to clarify the mechanism for the occurrence of unstable pellet-conveyance in PBT. Moreover, we studied the correlation between the friction coefficient and temperature of the pellets using a friction measuring machine, and obtained the following results(1) The visualization experiment confirmed that PBT pellets have a small axial velocity component and a large rotational velocity component compared with other resins, and showed an unstable velocity distribution with changes in the screw revolution rate. When the screw stagnated during the charging process, an airspace occurred temporarily in the solid-conveying area of the heating cylinder. At the same time axial velocity component of the pellet decreased while the rotational velocity component increased.(2) The friction measurements confirmed that the friction coefficient of the resin pellet depends mainly on the temperature. Moreover it was shown that the reverse motion of the screw during the charging process forms an inverse temperature area where the temperature of the screw surface becomes higher than that of the inside wall surface of the cylinder. From these results, it was suggested that unstable pellet-conveyance in PBT results from the changes in friction force balance in the solid-conveying region due to the both of the temperature reverse and the singularity of friction coefficient of PBT.

Stimulated emission of AKR in regions of a weakly unstable electron velocity distribution

It is generally believed that auroral kilometric radiation (AKR) originates in regions in which energetic auroral electrons possess a velocity distribution with a loss‐cone feature. According to the cyclotron maser theory of AKR, the resulting instability can be substantial in some regions of the auroral zone, leading to the generation of radiation with many features that are consistent with the observations. However, in situ measurements of velocity distributions obtained with satellites only show evidence of moderate positive gradients in the perpendicular velocity component υ⊥. Such distributions prove to be only marginally unstable, and thus imply a low level of radiation. From this point of view it is of interest to study the amplification of externally generated radiation. This radiation might originate from adjacent regions with a more unstable velocity distribution or from remote sources in space. In this work we perform numerical simulation studies using alternatively an observed electron velocity distribution, obtained from DE 1 measurements, and an idealized loss‐cone distribution. The results show the expected amplification of X mode radiation as well as effects which go beyond the behavior of a simple amplifying medium. Whereas wave growth is exponential for the idealized loss‐cone distribution, it is initially linear in time in the weakly unstable case, following the increase of the external wave power in the simulation. At later stages the collective properties of the plasma lead to interesting effects, such as the continuation of wave growth after cessation of the external wave in cases which do not exhibit growth otherwise, and a threshold power level before growth occurs. We suggest that these phenomena are relevant to the understanding of the observed enhancement and triggering of AKR due to solar radio bursts.

A kinetic study of solar wind mass loading and cometary bow shocks

A detailed numerical study is conducted to understand the kinetic processes associated with solar wind mass loading due to pickup of cometary ions and the formation of cometary bow shocks. Because in this study we are most interested in phenomena which take place over time and spatial scales associated with ion dynamics, electrons are treated as a massless fluid. On the other hand, solar wind protons and heavy cometary ions are treated kinetically. It is found that solar wind deceleration and pickup of cometary ions take place through both the macroscopic electromagnetic fields embedded in the solar wind, as well as the microscopic fields associated with low‐frequency electromagnetic waves that are generated by the unstable velocity distribution function of the cometary ions. These electromagnetic waves can grow to very large amplitudes and their nonlinear evolution is controlled by their wave normal angle. At parallel propagation where the waves are noncompressional, parametric instabilities seem to be operative, while the oblique, compressional waves are found to steepen and form shocklets. As for the nature of cometary bow shocks, three different regimes are found, based on the shock normal angle. For shock normal angles at or near 90° (quasi‐perpendicular), a typically thin transition region (shock) is formed through steepening of fast magnetosonic pulses. This shock is a pure proton shock in that no sharp change in density or velocity of the cometary ions is observed across the shock. At intermediate shock normal angles (oblique), a much wider transition region is seen where the solar wind is gradually heated and decelerated. This region, whose width is much larger than the gyroradius of cometary ions, is associated with a high level of turbulence due to ion pickup instabilities and is unlike a typical fast magnetosonic shock. Finally, at small shock normal angles (quasi‐parallel), a narrow transition region is found which is similar to a parallel terrestrial shock. The formation of this shock is not due to wave steepening but rather is the result of scattering and heating of the solar wind protons by the large‐amplitude electromagnetic waves that are generated through the relative drift between the protons and the cometary ions. These results are compared and shown to be in qualitative agreement with the recent observations at comets.

On the polarization, compression and nonoscillatory behavior of hydromagnetic waves associated with pickup ions

Newborn ions acquire highly unstable velocity distributions that, in the solar wind frame, might range from beam‐ to ring‐like. Solution of the kinetic dispersion equation shows that heavy pickup ions with large perpendicular energies excite a new hydromagnetic wave mode with maximum growth, high (magnetic field and mass density) compression ratios, and almost linear polarization coexisting slightly away (6° ‐ 15°) from parallel propagation. The mode arises from the coupling of the heavy ion beam to the modified left‐hand wave dispersion caused by the multi‐ion nature of the medium. The ion beam can also bring about nonoscillatory, purely growing structures distinct from the mirror wave through the coupling of a counter‐streaming left‐hand mode to a co‐streaming right‐hand wave. The free energy source parameters are varied to determine their relative influence and define the domain of existence of the instability. Its characteristics may prove helpful in the interpretation of recent cometary (Halley and Giacobini‐Zinner) and artificial release (AMPTE) observations.

Theory for the critical ionization velocity phenomenon

A theoretical consideration is given to the critical ionization velocity. A macroscopic theory is constructed, assuming that (1) the newly born ions have an unstable velocity distribution and (2) the resultant fluctuating electric field heats the electrons. For the critical ionization velocity to operate in the case of m aV 2 2 > eφ ion , the initial values of high speed ion (or newly ionized ion) density and suprathermal electron energy density should be above a certain threshold. This threshold depends upon the velocity diffusion co-efficient and the collisional loss rate of the newly ionized ion.

A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution

A numerical method for studying one-dimensional electron plasma evolution under typical interplanetary conditions is presented. The method uses the Fourier-Fourier transform approach to a plasma model which is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws which are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is introduced. These conservation laws are used to check the accuracy of the numerical solutions. A discretization error analysis is given. Two numerical instabilities and the methods used for their suppression are discussed. Several solution examples are presented. Two of these are comparisons with earlier independent results; the comparison is favorable. A third example is also discussed which uses an interplanetary observation of a bump-on-tail unstable velocity distribution as initial data. It is shown that in interplanetary plasma conditions the bump-on-tail instability leads to significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation in terms of wave-wave coupling during the growth phase of the instability is given.

Measurements on ionic waves amplified by collective behaviour in an alkali plasma

An experiment on ionic waves sustained by collective amplification in a uniform, steady plasma, free of electric field, is described. The plasma is obtained by contact ionization of caesium or potassium vapours on the surface of two coaxial tantalum cylinders kept at a temperature of about 2600 °K. The application of a variable D.C. voltage between the two cylinders gives rise to an unstable velocity distribution function which can be varied at will. Predictions are given for the dependence of the frequency of the oscillations on the applied voltage, on the ionic mass and on the plasma density. Experimental results are consistent with the predictions if the wavelength is equal to four times the distance between electrodes. A possible explanation of this fact is also suggested.