A linear stability analysis of large-Prandtl-number thermocapillary liquid bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4  Pr  50). We focus on the relationships between the critical Reynolds number Re_c, the azimuthal wave number m, the aspect ratio Γ and the Prandtl number Pr. A detailed Re_c–Pr stability diagram is given for liquid bridges with various Γ. In the region of Pr > 1, which has been less studied previously and where Re_c has been usually believed to decrease with the increase of Pr, we found Re_c exhibits an early increase for liquid bridges with Γ around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the “effective” part of liquid bridge.     

Steady and oscillatory convection in vertical cylinders heated from below. Numerical simulation of asymmetric flow regimes

Three-dimensional buoyancy driven flows in vertical cylinders are simulated with a finite difference technique. Asymmetric convective flows are studied for three values of the (length-to-radius) aspect ratio A. One result concerns the occurrence of asymmetric convection in a flat A=0.485 cylinder for Pr=6.7, near the threshold and up to 3Ra_c (where Ra_c is the critical Rayleigh number and Pr is the Prandtl number). Complex (steady and time-dependent) supercritical regimes have been simulated in cylinders of aspect ratios A=2 and A=4 for Pr=0.02 and in ranges of Ra up to 8Ra_c and 6Ra_c, respectively. The flow patterns are analysed graphically and discussed with respect to a weakly nonlinear analysis and to experiments. In a particular case, A=4 and Pr=0.02, an oscillatory motion has been obtained and some features of the flow pattern are shown during a period.     

进气旋流对推力喷管性影响的研究

介绍了模拟近代大涵道比发动机排气状况的旋流模型,和在喷管落压比1.2到6.5范围内,进气旋流对轴对称喷管,矩形收-扩喷管,楔形二元喷管,和单边膨胀斜板形喷管等性能和射流流态影响等的一些实验结果。实验数据指出:进气旋流可使喷管出口射流柱中的旋涡加强,射流与外界气流间的混合区扩大,中心核心流区缩小,但它对轴对称喷管出口流态的影响很小。进气旋流同时对喷管推力系数和流量系数均起不利影响,增大进气旋流角度会使喷管推力系数和流量都下降,特别是当旋流角超过某一“临界”值后二者降低很急剧,并且二元喷管降低的程度比轴对称喷管更严重,因之在具体应用情况中,保留多大发动机的旋流,要针对具体情况综合考虑各种因素来选定。     

Modelled ionospheric Te profiles at mid-latitudes for possible IRI application

The electron temperature (T_e) variation in the mid-latitude ionosphere at altitudes between 120 – 800 km has been modelled for various seasonal and solar-cycle conditions. The calculated electron temperatures are consistent with plasma densities and ion temperatures computed from a time-dependent ionospheric model. The T_e distribution can be represented by a subset of standard T_e profiles. T_e above 200 km is controlled by the magnetospheric heat flux into the ionosphere. For realistic values of the magnetospheric heat flux, the maximum electron temperature ranges from 3000 to 10,000 K at 800 km. The effect of increasing the heat flux is to increase the topside temperature but retain the profile shape. Hence, given a topside T_e observation and selection of an appropriate profile shape, the entire T_e distribution can be computed.     

Global comparison of the model results of GSM TIP with IRI for summer conditions

This paper presents the results of the numerical calculations thermosphere/ionosphere parameters which were executed with using of the Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP)and comparison of these results with empirically-based model IRI-2001. Model GSM TIP was developed in West Department of IZMIRAN and solves self-consistently the time-dependent, 3-D coupled equations of the momentum, energy and continuity for neutral particles (O₂, N₂, O), ions (O⁺, H⁺), molecular ions (M⁺) and electrons and largescale eletric field of the dynamo and magnetospheric origin in the range of height from 80 km to 15 Earth’s radii. The empirically derived IRI model describes the E and F regions of the ionosphere in terms of location, time, solar activity and season. Its output provides a global specification not only of N_e but also on the ion and electron temperatures and the ion composition. These two models represent a unique set of capabilities that reflect major differences in along with a substantial approaches of the first-principles model and global database model for the mapping ionosphere parameters. We focus on global distribution of the N_e, T_i, T_e and TEC for the one moment UT and fixed altitudes: 110 km, h_mF2, 300 km and 1000 km. The calculations were executed with using of GSM TIP and IRI models for August 1999, moderate solar activity and quiet geomagnetic conditions. Results present as the global differences between the IRI and GSM TIP models predictions. The discrepancies between model results are discussed.     

Nonlinear electromagnetic perturbations in a degenerate electron–positron plasma

Nonlinear propagation of fast and slow magnetosonic perturbation modes in an ultra-cold, degenerate (extremely dense) electron–positron (EP) plasma (containing non-relativistic, ultra-cold, degenerate electron and positron fluids) has been investigated by the reductive perturbation method. It is shown that due to the property of being equal mass of the plasma species (_me=_mp$m_e=m_p$, where _me$m_e$ and _mp$m_p$ are electron and positron mass, respectively), the degenerate EP plasma system supports the K-dV solitons which are associated with either fast or slow magnetosonic perturbation modes. It is also found that the basic features of the electromagnetic solitary structures, which are found to exist in such a degenerate EP plasma, are significantly modified by the effects of degenerate electron and positron pressures. The applications of the results in an EP plasma medium, which occurs in compact astrophysical objects, particularly in white dwarfs, have been briefly discussed.     

无振荡、无自由参数格式在数值模拟盔型磁场中太阳风流动的应用

提出了一种离散二维三分量理想磁流体力学守恒型方程组（MHD）的算法（NNDMHD），它有效地控制了磁场散度不为零误差对动量方程组的影响，把气体动力学中计算跨音速流动问题的有效算法——无振荡、无自由参数（NND）格式推广应用到MHD方程组中。利用该算法首先对常见一维和二维算例进行数值试验，得到比较好的结果，消除了间断处的非物理振荡。然后对太阳风在子午面轴对称盔形磁场位形中流动进行数值试验，在这个算例中，物理量沿径向变化大，NNDMHD格式仍然能够有效地控制磁场散度离散不为零误差导致的非物理流动。这个算例的计算结果表明：在网格划分比通常情况和稀4倍时，该算法仍保持很好的计算稳定性。     

Effect of gravity on coupled convective and interfacial instabilities during directional solidification

We investigate the role of gravity in a linear stability analysis of the onset of coupled convective and morphological instabilities during directional solidification at constant velocity of a dilute alloy of tin in lead. For solidification vertically upwards, the temperature gradient alone would cause a negative density gradient and the solute gradient alone would cause a positive density gradient. Two types of instability are found, a convective type that occurs for long wavelengths and a morphological type that occurs for short wavelengths. In general, these are coupled but the morphological instabilities are practically independent of gravity and thus correspond to the predictions of previous morphological stability theory in which density changes and convection are neglected. The convective instabilities depend strongly on gravity; for a growth velocity of V = 1 μm/s and a temperature gradient in the liquid of G_L = 200 K/cm, the critical concentrations for convective instabilities are 3.1 × 10^?4, 3.1 × 10^?2 and 2.39 wt. % for g_e = 980 cm/s², 10^?4 g_e and 10^?6 g_e, respectively. For low velocities, the convective instabilities occur at much lower solute concentrations than the morphological instabilities whereas at high velocities, the reverse is true. At intermediate velocities where the changeover takes place, there are oscillitory instabilities of mixed character whose periods range from 60 s at g_e to 6 × 10⁴ s at 10^?6 g_e.     

热毛细效应对细丝薄膜流动不稳定性的影响

根据重力与热毛细力耦合作用薄膜在细丝上的流动情况,采用长波近似推导了界面的演化方程.通过色散关系分析热毛细作用对Rayleigh-Plateau稳定性的影响;通过时空模式的稳定性分析,研究了系统的绝对对流不稳定性特性;通过直接数值模拟,研究了薄膜破裂和绝对对流稳定性的关系.      

Particle acceleration by stochastic fluctuations and dawn-dusk electric field in the Earth’s magnetotail

This work is devoted to investigate the interaction between protons and stochastic time-dependent electromagnetic fields generated by oscillating clouds of finite size, randomly positioned in the x–y  -plane. The geometry of the system is two-dimensional and, beside the time-dependent electromagnetic fluctuations, a steady-state, dawn-dusk electric field, _Ey$E_y$, has been added along the y-direction. The simultaneous presence of the stochastic time-dependent fluctuations and of the constant electric field component in the same system gives rise to two types of acceleration mechanisms operating on test particles: a second order Fermi-like process and a direct acceleration. By performing a parametric study, we extensively study the contribution of the two processes to proton acceleration. The energy values reached by test particles in this simple model are in good agreement with those observed in the Earth’s magnetotail region. Possible applications to the problem of particle acceleration in the terrestrial magnetosphere are widely discussed, and guidelines for future works are drawn.     

Solar cycle effects upon the relationship of Ne and Te in the F-region

Employing Atmsophere Explorer-C measurements made in 1974, just prior to solar minimum, Brace and Theis /1/ demonstrated that a remarkably consistent inverse relationship existed between the electron density N_e and temperature T_e in the F-region. In this paper we use later data from AE-C, taken when solar activity was rising (1975–1978), and Dynamics Explorer-2 data taken at solar maximum (1981), to examine how the temperature and density relationship changes with solar activity. We find that the solar maximum T_e is a factor of two larger than the solar minimum T_e for the same values of N_e. T_e does not necessarily increase with solar activity, however, because N_e increases enough to approximately cancel the effect of higher solar extreme ultraviolet heating. We find that the effect of solar activity can be accounted for by a simple function of the F_10.7 cm index that multiplies the solar minimum equation of Brace and Theis /1/.     

Ionospheric electron temperature at solar maximum

Langmuir probe measurements made at solar maximum from the Dynamics Explorer-2 satellite in 1981 and 1982 are employed to examine the latitudinal variation of electron temperature, T_e, at altitudes between 300 and 400 km and its response to 27 day variations of solar EUV. Comparison of these data with T_e models based on the solar minimum measurements from Atmosphere Explorer-C suggest that the daytime T_e does not change very much during the solar cycle, except at low latitudes where an especially large 27 day variation occurs. The 27 day component decreases from about 7°/F10.7 unit at the equator to 3°/F10.7 unit at 851V 3 middle and higher latitudes. From these DE-2 measurements, and those from AE-C, we conclude that the daytime T_e near the F₂ peak is more responsive to short-term (daily) variations in F10.7 than to any longer term changes that may occur between solar minimum and solar maximum. To investigate this sensitivity of the dayside ionosphere to solar activity we employ the inverse relationship of T_e and N_e, that was found at solar minimum, to see if it can be used to order the T_e behaviour at solar maximum. We introduce a simple quadratic correction for the F10.7 influence on T_e based on the entire daytime AE-C and DE-2 data base between 300 and 400 km. Although this equation may be found useful, the systematic deviations of the DE-2 data suggest that the solar minimum model does not accurately describe the T_e-N_e relationships at solar maximum, at least above 300 km where the DE-2 measurements were made. Future work with this data base should attempt to see if such a relationship exists.     

Melt temperature fluctuations: Causes and response of the solidification front

It is well understood that temperature oscillations and fluctuations during melt growth give rise to fluctuating concentration of solute in the crystal — so-called solute (or impurity) striations. A major source of the temperature fluctuations is the transition to turbulence in the melt resulting from strong buoyancy and/or surface-driven flows. The interaction of these natural convective flows with any imposed rotation is of significance. The major factors causing flow transitions and particularly those which lead to time-dependent flows in Czochralski and float-zone melts will be briefly reviewed and the likely influence of a low-g environment considered. Theoretical analysis and experimental study of the response of the crystal-melt interface to such temperature fluctuations is reviewed and criteria for maximising crystal homogeneity discussed.     

Surface tension-driven flows in horizontal liquid metal layers

The problem of surface tension-driven flows in horizontal liquid layers has been studied experimentally, and theoretically by direct numerical simulation and small perturbation analysis. We focus our attention on situations in which the depth of the fluid (liquid tin; small Prandtl number, Pr=0.015) is small enough to ensure the predominance of the surface tension forces over those due to the buoyancy. The surface velocity has been experimentally obtained for liquid tin layer with various aspect ratio (length to height) in the range 5<A<83. The thermal gradients are ranged from 5 to 40°K/cm. In the numerical study, the Navier-Stokes and energy equations are solved by an efficient finite difference technique. The parameters governing the flow behaviour in the liquid are varied to determine their effects on thermocapillary convection: the Reynolds number 10<Re<210⁴ and the aspect ratio 2<A<25; with Pr kept constant at Pr=0.015. The linear eigenequation resulting from small spatial disturbances of the Couette flow solution is solved using an Tau-Chebyshev approximation. A notable feature of the theoretical study is the totally different end circulations. In the region near the cold wall a multicell structure is evident. This agrees with the eigensolution which is of complex type, indicating spatial periodicity. In the hot wall region the flow is accelerated to reach the velocity value for the fully-developed Couette flow which is reached under conditions such as Re/A<20. The transition from viscous to boundary layer regime occurs for a critical value (Re/A)_c of nearly about 200, as deduced from the numerical and experimental results.     

On the physical state in the narrow-line region of the classical Seyfert galaxy NGC 7469

Based on the spectrophotometric data, by decomposition of the observed continuum, the power - law continuum characteristics of the central source are obtained. The behaviour of both electron temperature T_e and density n_e in the Narrow - Line Region (NLR) of NGC 7469 is discussed on the thermal and ionization equilibria calculations. T_e in NLR of the Sy1 galaxies are higher than the Sy2 ones, and the possible explanation is the lack of the dense (n_e 10¹⁰ cm⁻³) zone close to the central source in the Sy2 galaxies.     

Dynamical evolution of high area-to-mass ratio debris released into GPS orbits

A large set of simulations, including all the relevant perturbations, was carried out to investigate the long-term dynamical evolution of fictitious high area-to-mass ratio (A/M) objects released, with a negligible velocity variation, in each of the six orbital planes used by Global Positioning System (GPS) satellites. As with similar objects discovered in near synchronous trajectories, long lifetime orbits, with mean motions of about 2 revolutions per day, were found possible for debris characterized by extremely high area-to-mass ratios. Often the lifetime exceeds 100 years up to A/M ∼ 45 m²/kg, decreasing rapidly to a few months above such a threshold. However, the details of the evolution, which are conditioned by the complex interplay of solar radiation pressure and geopotential plus luni-solar resonances, depend on the initial conditions. Different behaviors are thus possible. In any case, objects like those discovered in synchronous orbits, with A/M as high as 20–40 m²/kg, could also survive in this orbital regime, with semi-major axes close to the semi-synchronous values, with maximum eccentricities between 0.3 and 0.7, and with significant orbit pole precessions (faster and wider for increasing values of A/M), leading to inclinations between 30° and more than 90°.     

Latitudinal variation of the topside electron temperature at different levels of solar activity

A database of electron temperature (T_e) measurements comprising of most of the available satellite measurements in the topside ionosphere is used for studying the solar activity variations of the electron temperature T_e at different latitudes, altitudes, local times and seasons. The T_e data are grouped into three levels of solar activity (low, medium, high) at four altitude ranges, for day and night, and for equinox and solstices. We find that in general T_e changes with solar activity are small and comparable in magnitude with seasonal changes but much smaller than the changes with altitude, latitude, and from day to night. In all cases, except at low altitude during daytime, T_e increases with increasing solar activity. But this increase is not linear as assumed in most empirical T_e models but requires at least a parabolic approximation. At 550 km during daytime negative as well as positive correlation is found with solar activity. Our global data base allows to quantify the latitude range and seasonal conditions for which these correlations occur. A negative correlation with solar activity is found in the invdip latitude range from 20 to 55 degrees during equinox and from 20 degrees onward during winter. In the low latitude (20 to −20 degrees invdip) F-region there is almost no change with solar activity during solstice and a positive correlation during equinox. A positive correlation is also observed during summer from 30 degrees onward.     

Marangoni convection when the surface tension increases with the temperature in normal and low gravity conditions

Thermocapillary convection has been studied in n-heptanol aqueous solutions whose surface tension is increasing with the temperature.

The fluid was confined in a parallelipipedic enclosure and a thermal gradient was imposed parallel to the free liquid/gas interface. The motions induced by the thermocapillary forces have been studied under low gravity conditions during Texus sounding rocket experiments and during the Spacelab D1 mission.

The combined thermocapillary and buoyancy convection have been extensively studied during ground based experiments.

The influence of the aspect ratio and of the alcohol concentration were investigated. Detailed velocity field was determined at the steady state under normal gravity conditions by Laser Doppler Anemometry (LDA).

The aspect ratio was of 0.3 and the temperatures imposed to the lateral sides of the cell were respectively 45°C and 60°C. With these experimental conditions, two superposed contrarotative cells were observed with rapid motions in the surface from the cold to the hot side. This convective pattern was also observed during the normal and high gravity periods of parabolic flights but during the low gravity period of the parabola the motions stopped everywhere in the fluid even in the surface and reappeared immediatly at the pull out of the parabola.