Oscillatory binary fluid convection in large aspect-ratio containers

Direct numerical simulations of chevrons, blinking states, and repeated transients in binary fluid mixtures with a negative separation ratio heated from below are described. The calculations are performed in two-dimensional containers for experimental parameter values and boundary conditions. Quantitative agreement with the experiments of Kolodner [Phys. Rev. E 47, 1038 (1993)] is obtained, and the origin of the blinking and repeated transient states is elucidated.     

Numerical simulations of binary fluid convection in large aspect ratio annular containers

The patterns arising in large aspect ratio annular containers heated from below are analyzed for water-ethanol mixtures with negative Soret coupling. The subcritical Hopf bifurcation at the onset of convection leads to a very rich dynamics. Using high resolution numerical tools based on spectral methods to solve the hydrodynamic equations we obtain and review the properties of the different regimes arising in early stages of convection: spatially extended stationary and travelling wave convective roll structures, dispersive chaotic states, and several types of localized convection. The dynamics triggered by the Eckhaus–Benjamin–Feir instability is presented for a mixture with a moderate negative value of the separation ratio.     

An eight-mode lorenz model of travelling waves in binary fluid convection

An eight-mode truncation of a model of binary fluid convection, allowing travelling wave solutions, is introduced. Qualitatively new dynamics is found, in much closer correspondence with recent experiment than a previous five-mode truncation that is restricted to standing waves.     

混合流体Rayleigh-Benard行波对流中的缺陷结构

通过流体力学基本方程的数值模拟,研究了含有缺陷的行波对流的动力学特性. 当分离比Ψ＝－06时,随着相对瑞利数r逐渐增加,系统由局部行波对流过渡到含有缺陷的行波对流,然后缺陷消失过渡到无缺陷的行波对流. 对于不同分离比的研究表明,缺陷出现的周期随着分离比减小而迅速增加,随着r增加而增加. 在负的小分离比时的增加速率大于大分离比时的增加速率. 缺陷存在区间Δr随着分离比绝对值减小很快变小, 并且当Ψ＝－011时缺陷消失,没有发现含有缺陷的行波对流. 当r大于Δr的上限时,系统过渡到无缺陷的行波对流.可是,当r小于Δr的下限时,不同的分离比Ψ值,对应不同的行波对流斑图. 这说明分离比明显地影响着各斑图形成及它们之间的转换,斑图之间的转换是很复杂的. 关键词： Rayleigh-Benard对流 缺陷 混合流体 行波     

双组分混合流体中Eckhaus不稳定调谐的行波对流

在双组分混合流体的Rayleigh-Bénard对流系统中，数值模拟获得了周期性时空位错缺陷调谐的扩展行进波对流状态.研究了该状态的时空演化特性.结果表明，Eckhaus不稳定触发的对流涡卷对的产生是调谐的起源，对流涡卷在边界处生成与湮没频率的不同，又使系统返回不稳定区域，系统在稳定与不稳定的波数之间振荡.还探讨了一个周期内传热与混合特性的改变及其控制参数的变化规律. 关键词： 双组分混合流体 行波对流 时空位错缺陷 Eckhaus不稳定调谐     

Unstable periodic solution controlling collision of localized convection cells in binary fluid mixture

We study the collision processes of spatially localized convection cells (pulses) in a binary fluid mixture by the extended complex Ginzburg-Landau equations. Both counter- and co-propagating pulse collisions are examined numerically. For counter-propagating pulse collision, we found a special class of unstable time-periodic solutions that play a critical role in determining the output after collision. The solution profile right after collision becomes close to such an unstable pattern and then evolves along one of the unstable manifolds before reaching a final destination. The origin of such a class of unstable solutions, called scattors, can be traced back to two-peak bound states which are stable in an appropriate parameter regime. They are destabilized, as the parameter is varied, and become scattors which play the role of separators of different dynamic regimes. Delayed feedback control is useful to detect them. Also, there is another regime where the origin of the scattors is different from that of the above case. For co-propagating pulse collision, it is revealed that the result of pulse collision depends on the phase difference between pulses. Moreover, we found that a coalescent pulse keeps a profile of two-peak bound state, which is not observed in the case of counter-propagating pulse collision. Complicated collision dynamics become transparent to some extent from the viewpoint of those unstable objects.     

Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong soret effect

Spatially confined solutions of traveling convection rolls are determined numerically for binary mixtures such as ethanol-water. The appropriate field equations are solved in a vertical cross section of the rolls perpendicular to their axes subject to realistic horizontal boundary conditions. The localized convective states are stably and robustly sustained by strongly nonlinear mixing and complex flow-induced concentration redistribution. We elucidate how this enables their existence for strongly negative separation ratios at small subcritical heating rates below the saddle node of extended traveling convection rolls where the quiescent fluid is strongly stable.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

Analytical and numerical exploration of oscillatory convection in porous media

This study is part of the research about the influence of the thermal gradient on the composition and the stability of fluids in geological environments. This paper presents modelling results of oscillatory convection in a porous medium using the METSOR code. The model solves the heat and mass transport equations in a porous medium and takes into account the Soret effect (mass transport under thermal gradient). Oscillatory convection may occur in pure fluids and in binary mixtures (as a consequence of the Soret effect). Experimental data confirm the existence of this phenomenon in porous media. Here, the outputs of the METSOR code are verified against existing analytical solutions. A first modelling attempt of oscillatory convection in mixtures is presented (salt aquifer).     

On the brink of jamming: granular convection in densely filled containers

Granulates are ubiquitous in nature and technology, but, despite their great importance, their dynamics are by far less well understood than those of liquids. We demonstrate in an almost compactly filled flat (Hele-Shaw) cell, where slow horizontal rotation simulates a variable gravitational force, that unexpected dynamic structures may arise under geometrical restrictions. The cell motion drives regular flow in the compact interior, and convection rolls combine with segregation. The container fill level is crucial for the dynamic regime. A transition from chute flow at lower fill levels to convection in densely packed containers is found. These observations suggest the existence of comparable phenomena in situations where so far no systematic search for dynamic patterns has been performed.