Realistic rotating convection in a DNA suspension

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation for realistic rigid-rigid boundary conditions. We focus our analysis in the DNA aqueous suspensions. Instability thresholds for oscillatory convection are calculated. Finally, we analyze the stabilizing effect for the onset of convection.     

Thermal convection in a rotating binary viscoelastic liquid mixture

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation. In particular, we focus in the Maxwelian case of viscoelastic fluid. We obtain explicit expressions for the convective thresholds in terms of the mixture parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic rigid–rigid boundary conditions.     

Bénard-Marangoni instability in a viscoelastic ferrofluid

In this paper we report theoretical and numerical results on convection of a magnetic fluid in a viscoelastic carrier liquid. The viscoelastic properties are given by the Oldroyd model. We impose the lower interface to be rigid, whereas the upper one is free and is assumed to be non-deformable and flat. Also, at the upper interface the surface tension is taken to vary linearly with the temperature. Using a spectral method we calculate numerically the convective thresholds for both stationary and oscillatory bifurcations. The effect of the viscoelasticity and the Kelvin force on the instability thresholds are emphasized.     

Enhanced vertical inhomogeneity in turbulent rotating convection

In this Letter we report experimental evidence that rotation enhances vertical inhomogeneity in turbulent convection, in spite of the increased columnar flow ordering under rotation. Measurements using stereoscopic particle image velocimetry have been carried out on turbulent rotating convection in water. At constant Rayleigh number Ra=1.11 x 10(9) several rotation rates have been used, so that the Rossby number takes values from Ro=infinity (no rotation) to 0.09 (strong rotation). The three-component velocity data, obtained at two vertical positions, are used to investigate the anisotropy of the flow through the invariants of the Reynolds-stress anisotropy tensor and the Lumley triangle, as well as to correlate the vertical velocity and vorticity. In the center plane rotation causes the turbulence to be "rodlike," while closer to the top plate a trend toward isotropy is observed.     

数值分析环形池硅熔体旋转-热毛细对流及其稳定性

数值模拟了内半径20 mm、外半径40 mm、深5 mm环形池内硅熔体在旋转和热毛细力共同驱动下的热对流,通过线性稳定性分析确定了旋转-热毛细对流失稳的临界Marangoni数等临界条件。研究结果表明,液池低速旋转会降低轴对称热毛细对流的稳定性,而较高速度的旋转能增强热毛细对流的稳定性。临界条件下旋转-热毛细对流耗散结构波纹的传播方向与液池的旋转方向相同,临界周向波数随旋转速度的增加而增加。在较大的旋转速度下,液池底部出现涡胞,底部涡胞对热毛细对流的稳定性具有削弱作用。     

Thermal convection thresholds in a Oldroyd magnetic fluid

We report theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid. The viscoelastic properties is given by the Oldroyd model. We obtain explicit expressions for the convective thresholds in terms of the parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic boundary conditions. The effect of the Kelvin force and of the rheology on instability thresholds for a diluted suspensions are emphasized.     

Stationary thermal convection in a viscoelastic ferrofluid

We report theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid. We focus in the stationary convection for idealized boundary conditions. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system. Close to bifurcation, the coefficients of the corresponding amplitude equation are determined analytically. Finally, the secondary instabilities are performed.     

Instabilities and spatio-temporal chaos of long-wave hexagon patterns in rotating Marangoni convection

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side band instabilities. In the presence of rotation, steady and oscillatory instabilities are identified. One of them leads to stable, homogeneously oscillating hexagons. For sufficiently large rotation rates the stability balloon closes, rendering all steady hexagons unstable and leading to spatio-temporal chaos. (c) 2002 American Institute of Physics.     

Drifting convection cells in rotating fluid layers heated from below

It is shown that hexagonal convection cells in a rotating horizontal fluid layer heated from below will in general exhibit a drift in contrast to convection rolls except in the case of a vertical axis of rotation. The direction of the drift is prograde (retrograde) for cells with rising (descending) motion in the center of the convection cell. In addition a mean flow generated by convection is derived. An application to solar convection is discussed.     

Thermosolutal convection in a Maxwellian viscoelastic fluid in porous medium

The thermosolutal convection in a layer of Maxwellian viscoelastic fluid heated and soluted from below in porous medium is considered. The effects of uniform magnetic field and uniform rotation on the thermosolutal convection are also considered. For stationary convection, the Maxwellian viscoelastic fluid behaves like a Newtonian fluid. The sufficient conditions for the nonexistence of overstability are obtained. The critical Rayleigh number is found to increase with the increase in magnetic field, rotation and stable solute gradient.     

Determination of forced convection parameters by interferometric imaging of the concentration field during growth of KDP crystals

Growth of a potassium dihydrogen phosphate (KDP) crystal from its aqueous solution has been considered under forced convection conditions. The KDP crystal is grown in a conventional top hanging geometry. Forced convection conditions are created by rotating the crystal about a vertical axis. The rotational RPM is varied in a cycle, creating an accelerated rotation (AR) paradigm. The effect of varying the rotational RPM on the concentration field around the crystal was investigated. Mach-Zehnder interferometry was adopted as an optical technique to image the evolving concentration fields. Six different experiments were performed to obtain the specific set of time periods and rotation rates of the acceleration cycle that result in a uniform concentration field around the growing crystal. The Reynolds number, an index of the strength of forced convection, was optimized through the experiments. The optimized parameters of the accelerated rotation cycle were found to be as follows: maximum rotation rate of 32 RPM, spin up period=40 s, spin down period=40 s, steady period=40 s, and stationary period=40 s. The parametric study further revealed that concentration was highly sensitive to the maximum rotation rate adopted during the AR cycle. It did not depend crucially on the time periods that could be varied by as much as ±25% around the respective average values. Finally, a KDP crystal was grown using the optimized forced convection parameters and the crystal quality was found to be good.     

Influence of the meridional flow and thermomagnetic convection on characteristics of magnetic fluid seal

For the low-speed magnetic fluid seals, the influence of the meridional flow, induced by the shaft rotation, on the distribution of magnetic particles concentration, is studied. Influence of the thermomagnetic convection on the structure of this flow and on the temperature distribution in high-speed magnetic fluid seals is investigated also. The problems were examined by numerical methods. It is discovered that even very slow rotation of the shaft homogenises distribution of the magnetic particles concentration in the seal and thereby enlarges its operation life. For high-speed seals thermomagnetic convection provides the penetration of the fluid flow in the region of the narrow gap and levels off the temperature distribution decreasing its maximum value and thereby enlarges its operation life too. It is found also that the influence of thermomagnetic convection grows with the viscosity increasing.     

On thermal convection in slowly rotating systems

The dynamical properties of convection patterns in a fluid layer heated from below and rotating slowly about a horizontal axis are reviewed. Applications to the equatorial regions of planetary and stellar atmospheres are emphasized. Attention is drawn to the wavelike drift of hexagonal convection cells in the azimuthal direction and to the mean flow generated by all convection patterns except for rolls aligned with the axis of rotation.     

弱熔体对流对定向凝固中棒状共晶生长的影响

利用渐近方法求出在弱对流熔体中定向凝固棒状共晶生长的浓度场的渐近解,研究了弱熔体对流对定向凝固中棒状共晶生长的影响.结果表明,弱熔体对流对定向凝固中棒状共晶生长有显著的作用;平均界面过冷度不仅与棒状共晶的棒间距、生长速度有关,还与流动强度有关;当生长速度一定时,随着流动强度增大,棒状共晶的平均界面过冷度减小.利用最小过冷原则,获得棒间距与生长速度和流动强度的关系.结果表明,当生长速度比较小时,随着流动强度增大,棒状共晶的棒间距增大;当生长速度比较大时,随着流动强度增大,棒状共晶的棒间距变化减弱;棒状共晶的生长速度越小,流动对棒状共晶生长的影响越大.利用本文的解析结果计算在对流条件下Al-Cu共晶的棒间距,结果显示随着转速增大或径向距离增大,共晶的间距增大,这与Junze等的实验结果相符合.     

The meridional circulation of the Sun: Observations,theory and connections with the solar dynamo

The meridional circulation of the Sun, which is observed to be poleward at the surface, should have a return flow at some depth. Since large-scale flows like the differential rotation and the meridional circulation are driven by turbulent stresses in the convection zone, these flows are expected to remain confined within this zone. Current observational(based on helioseismology)and theoretical(based on dynamo theory) evidences point towards an equatorward return flow of the meridional circulation at the bottom of the convection zone. Assuming the mean values of various quantities averaged over turbulence to be axisymmetric,we study the large-scale flows in solar-like stars on the basis of a 2D mean field theory. Turbulent stresses in a rotating star can transport angular momentum, setting up a differential rotation. The meridional circulation arises from a slight imbalance between two terms which try to drive it in opposite directions: a thermal wind term(arising out of the higher efficiency of convective heat transport in the polar regions) and a centrifugal term(arising out of the differential rotation). To make these terms comparable,the poles of the Sun should be slightly hotter than the equator. We discuss the important role played by the meridional circulation in the flux transport dynamo model. The poloidal field generated by the Babcock-Leighton process at the surface is advected poleward, whereas the toroidal field produced at the bottom of the convection zone is advected equatorward. The fluctuations in the meridional circulation(with coherence time of about 30-40 yr) help in explaining many aspects of the irregularities in the solar cycle. Finally, we discuss how the Lorentz force of the dynamo-generated magnetic field can cause periodic variations in the large-scale flows with the solar cycle.     

Supercritical convection associated with ultrafast MHD rotation

Highly nonlinear buoyant convection is investigated analytically under conditions typically encountered in the liquid cores of planets in the solar system. As a result of the supercritical behavior (enormous Rayleigh number) and ultrafast rotation (small Ekman number) typical of such flows, diffusion and viscosity act only in layers that are asymptotically thin in comparison with the radius of the core. These boundary layers control the buoyancy, the large-scale velocity, and the magnetic field observed at the planetary surface. The interchange of the internal layers determines the small-scale (unobservable) fields and the prevailing symmetry of the large-scale magnetic fields. It is proved for the first time that axisymmetric azimuthal flows dominate at large scales, while convection cells elongated parallel to the axis of rotation dominate at small scales. A system of equations is derived which is optimum for describing magnetoconvection of planetary cores on both large and small scales. It yields estimates in superb agreement with expensive numerical and experimental models of supercritical convection associated with rapid rotation. Such models will be capable of solving the MHD dynamo problem only when their algorithms are made consistent with the asymptotic limits presented here. Zh. éksp. Teor. Fiz. 115, 1708–1720 (May 1999)     

Rotating surface solitons

We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast with nonrotating waves, for high rotation frequencies they do not exhibit power thresholds for their existence. There exists an upper limit for the surface wave rotation frequency, which depends on the radius of the outer guiding ring and on its depth.     

Linear stability analysis of the natural convection in inclined rotating parallel plates

The linear stability analysis of the natural convection in a rectangular tilted infinite cavity filled with a Boussinesq fluid subject to Coriolis force is presented. The bottom and top surfaces have fixed temperatures. Both unstable and stable thermal conditions are studied (heated from below and heated from above respectively). The rotation axis passes through the center and it is orthogonal to the hot and cold surfaces. The stability equations were solved using the Tau–Chebyshev spectral method. The critical Rayleigh number and critical wave number were obtained for several rotation rates and different orientation of convective oblique rolls in a range of inclination of the cavity from 0 to 120 degrees. The stability analysis show that rotation rate affects the basic velocity profile, onset of convection, wave number and critical orientation of convective rolls.