The Onset of Convection in an Inclined Anisotropic Porous Layer with Oblique Principle Axes

We consider the onset of convection in an inclined anisotropic porous layer heated from below. To date the principle axes of the permeability and diffusivity tensors have been assumed to be aligned with the coordinate directions. Therefore particular emphasis is laid upon how the basic flow and criteria for the onset of convection are altered by the presence of oblique principle axes. When these axes are not aligned with the coordinate directions and when the ratios of the principle permeabilities or diffusivities are not too large or too small, we find that there is always a smooth transition in the orientation of the most dangerous mode of instability as the inclination increases from the horizontal. In more extreme cases there may be sudden changes in the orientation, Darcy–Rayleigh number and wavenumber.     

自然对流边界层中湍流的发生

自然对流边界层中从层流到湍流的转捩经历了浮力振型、无摩擦振型和黏性振型的三重流动不稳定性相继产生的前转捩过程,以及近壁迅速出现强湍流源,随之平缓地向自模拟的湍流边界层过渡的热转捩过程.浮力振型在修正Grashof数G>40时开始失稳并成为主要振型,在振幅分布中3种振型的临界层位置处出现3个峰值;在G>100时浮力振型消失,无摩擦振型失稳并成为主要振型,振幅分布中在近壁区还出现黏性振型的峰值;在G>170时无摩擦振型经非线性演化在外层形成较弱的湍流,但内层黏性应力仍远高于湍流应力,振幅分布中仅有与黏性振型相应的峰值,在频谱中黏性振型的基频、第一、第二、第三阶亚谐频随G的增加相继出现,此时黏性不稳定波的高频成分已转化为湍流,但低频成分仍按线性规律增长,直至湍流惯性子区开始形成;至G>800时黏性振型消失,并在G=850附近时近壁区出现强湍流源,湍流应力、湍能产生项和近壁湍流热流率剧增.在热转捩后期,湍流应力和湍能产生项明显下降,流动在内外层趋于平衡.     

Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

Allowing for the plastic properties of rock in stability problems for a stratified rock mass

The paper addresses the important issue of allowing for the inelastic properties of rock in stability problems for a stratified rock mass. A three-dimensional nonlinear problem statement is used. An exact method to study the surface instability of a regularly layered semi-infinite medium is developed. New numerical results are obtained __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 68–81, December 2007.     

The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper, we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the “near-flip” instability, we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.      

“Frictionless” and “frictional” ThermoElastic Dynamic Instability (TEDI) of sliding contacts

Recently, we found that a new form of coupled instability, named ThermoElastic Dynamic Instability (TEDI), can occur by interaction between frictional heating and the natural dynamic modes of sliding bodies. This is distinct from the classical dynamic instabilities (DI) which is produced by an interaction between the frictional forces at the sliding interface and the natural modes of vibration of the bodies if the friction coefficient is sufficiently high, and also from ThermoElastic Instability (TEI), which is due to the interaction of frictional heating and thermal expansion, leading for example to low pitched brake noise above some critical speed. This result was relative to an highly idealized system, comprising an elastic layer sliding over a rigid plane including both dynamic and thermoelastic effects, but neglecting shear waves at the interface due to frictional tractions (from which the denomination “frictionless TEDI”). We demonstrate here that including these shear waves destabilizes both the shear and dilatational vibration modes of the system at arbitrarily small friction coefficients and speeds, where DI and TEI are predicted to be stable. A detailed study of the new modes and transient simulations show that for low pressures and high speed, the system tends towards the results of the previous model (“frictionless TEDI”), i.e. the tendency to a state in which the layer bounces over the plane, with alternating periods of sliding contact and separation. In the case of low speeds and high pressures, viceversa, the system is dominated by the modes near the resonance of the shear and dilatational modes, with a resulting complex behaviour, but generally leading to stick-slip regimes, reducing the jumping mode of “frictionless TEDI”, because stick reduces or stops frictional heating production.     

槽道纤维悬浮流稳定性的实验研究

对槽道纤维悬浮流进行染色线流动显示和流场PIV实验测量,实验中选用的是直径为20μm、长径比为20～100的尼龙纤维。PIV2100处理器被用来加工处理采集的实验数据。槽道长度1.5m,横截面为矩形,尺寸为105×19mm。实验结果说明在Reynolds数相同的情况下,纤维悬浮流比对应的牛顿流更不容易失稳,悬浮流中的纤维起着抑制流场失稳的作用,而且随着纤维体积分数和长径比的增大,抑制失稳的程度也提高。扰动衰减率的最小值随纤维体积分数和长径比的增加而增大,这一效果在大Re数时更明显。     

Convective Instability in Superposed Fluid and Porous Layers with Vertical Throughflow

A closed form solution to the convective instability in a composite system of fluid and porous layers with vertical throughflow is presented. The boundaries are considered to be rigid-permeable and insulating to temperature perturbations. Flow in the porous layer is governed by Darcy–Forchheimer equation and the Beavers–Joseph condition is applied at the interface between the fluid and the porous layer. In contrast to the single-layer system, it is found that destabilization due to throughflow arises, and the ratio of fluid layer thickness to porous layer thickness, , too, plays a crucial role in deciding the stability of the system depending on the Prandtl number.     

Numerical study of buoyancy- and thermocapillary-driven flows in a cavity

Thermocapillary- and buoyancy-driven convection in open cavities with differentially heated endwalls is investigated by numerical solutions of the two-dimensional Navier-Stokes equations coupled with the energy equation. We studied the thermocapillary and buoyancy convection in the cavities, filled with low-Prandtl-number fluids, with two aspect-ratiosA=1 and 4, Grashof number up to 10⁵ and Reynolds number ⋎Re⋎≤10⁴. Our results show that thermocapillary can have a quite significant effect on the stability of a primarily buoyancy-driven flow, as well as on the flow structures and dynamic behavior for both additive effect (i.e., positiveRe) and opposing effect (i.e., negativeRe).     

薄膜沿加热平板下落的稳定性分布

本文分析了薄膜沿加热平板下落的稳定性。在时间模式下，发现流动的不稳定性是由表面波不稳定和加毛细不稳定构成的，同时当流体的热扩散越大以及界面热量损失越小时，热毛细不稳定越剧烈，在时空模式下，流动随着Marangoni数的增大。流动有可能从对流不稳定过渡到绝对不稳定，这一结论尚待实验验证。