可压缩流体的Rayleigh-Taylor和Kelvin-Helmholtz不稳定性

在状态方程为压力是密度的任意单值函数形式情况下，运用小扰动分析和奇异摄动法，给出了流体微扰方程渐近解和界面不稳定性的色散关系. 分析表明：对Rayleigh-Taylor不稳定性，在重力场作用下流体可压缩性形成的密度分布是致稳因素；而扰动流体的膨胀收缩效应助长不稳定性的发展；上层重流体的可压缩性是稳定因素，下层轻流体可压缩性是失稳因素. 而对Kelvin-Helmholtz不稳定性，流体可压缩性助长扰动的发展，是不稳定因素.     

可压缩性对Rayleigh-Taylor不稳定性的影响

对于状态方程为压力是密度的任意单值函数的理想流体 ,导出了Rayleigh Taylor不稳定性色散关系的一般形式。它表明 :较重流体易压缩是稳定因素 ,较轻流体易压缩是不稳定因素。可压缩性在重力场作用下形成的密度分布是稳定性因素 ,而膨胀压缩效应是不稳定因素。     

高Bond数下黏性液滴的Rayleigh-Taylor不稳定性

给出了高Bond数下黏性液滴表面Rayleigh-Taylor线性不稳定性的分析解，这种不稳定性对于超音速气流作用下液滴破碎的早期阶段起着至关重要的作用．基于稳定性分析的结果，导出了用于估算稳定液滴的最大直径及液滴无量纲初始破碎时间的计算式，这些计算式与相关文献给出的实验和分析结果比较显示了良好的一致．     

有限厚度流体层界面运动Rayleigh-Taylor不稳定性的数值模拟

采用二阶ＴＶＤ格式及ＬｅｖｅｌＳｅｔ方法计算了二维可压缩有限厚度流体层Ｒａｙｌｅｉｇｈ Ｔａｙｌｏｒ流体不稳定性。计算结果与Ｔａｙｌｏｒ的线性解和Ｏｔ的薄层非线性解析解符合很好。     

孔隙流体耦合效应对射流冲击应力分布的影响分析

运用全解耦流固耦合理论,建立了水射流冲击岩石介质流固耦合数值分析模型,给出了数值算法,计算分析了考虑和不考虑孔隙流体耦合效应对射流冲击岩石时应力分布的影响规律。结果表明,在射流冲击作用下,如不考虑孔隙流体耦合作用,最大拉应力位于冲击面,离冲击中心径向距离与喷距成正比,最大剪切应力位于岩石冲击中心下部约0.5倍喷嘴直径位置;如考虑孔隙流体耦合作用,最大拉应力位于岩石冲击中心下部约0.4倍喷嘴直径位置。数值分析结果可为水射流破岩机理研究中岩石破坏准则的选择提供依据。     

Richtmyer-Meshkov不稳定性流体混合区发展的实验研究

使用矩形激波管,在马赫数分别为$M=1.5$和1.7的条件下实验研究了气/液界面 上(即Atwood数$A$接近1时)由Richtmyer-Meshkov不稳定性引起的流体混合现象. 得到 了气/液界面上Richtmyer-Meshkov不稳定性后期流体混合区域宽度随时间的发展呈现出线 性关系的结果,即$h \propto t$. 比较了不同马赫数和初始扰动下的发展情况,发现当 马赫数增加时,同一时间混合区域 宽度随之增加,混合区域宽度增长变快;而相比于波长差别不大的弱多模态初始扰动(无人 为干扰界面), 当界面初始扰动获得随机外界干扰时,界面混合区域具有较大的宽度以及增 长速度. 并且增加激波马赫数和初始扰动多模态性,流体混合程度更为剧烈.     

黏弹性流体纯弹性不稳定现象研究综述

近年来粘弹性流体流动的弹性不稳定性现象引起了越来越多学者的关注与研究,与牛顿流体惯性不稳定现象不同,这种现象是由粘弹性流体流动中的弹性应力和粘性力之间相互作用,使得在较低的雷诺数下即可产生复杂的流动分岔不稳定现象。当流动中的弹性数（表现为 Deborah 数 De 与Reynolds 数Re 的比值,其中 De 数定义为粘弹性流体的松弛时间和流动的特征时间的比值,Re 数表征流动中惯性力与粘性力之比）较大时,在 Re<相似文献   

用浮阻力模型研究Richtmyer-Meshkov不稳定性诱导混合

采用浮阻力模型对激波管低压缩和激光加载高压缩情况下的Richtmyer-Meshkov不稳定性诱导混合现象进行了研究。通过与实验和理论分析结果进行比较发现:为了达到好的吻合, Richtmyer-Meshkov不稳定性情况下阻力系数的取值范围(2.0~5.36)比Rayleigh-Taylor不稳定性情况下的值(3.3~4.0)宽得多; 而在Richtmyer-Meshkov不稳定性情况下, 高压缩时阻力系数的不确定度(约为3.36)明显高于低压缩时的值(约为1.46), 模型的进一步完善还有待于更精确实验的验证。研究显示:指数律经验公式中指数随工况的不同而显著变化, 目前工程设计中采用指数律经验公式是粗糙的。     

低密度流体界面不稳定性大涡模拟

采用拉伸涡亚格子尺度应力模型对湍流输运中的亚格子作用项进行模式化处理,发展了适用于可压多介质黏性流动和湍流的大涡模拟方法和代码MVFT（multi-viscous flow and turbulence）。利用MVFT代码对低密度流体界面不稳定性及其诱发的湍流混合问题进行了数值模拟。详细分析了扰动界面的发展,流场中冲击波的传播、相互作用、湍流混合区边界的演化规律,以及流场瞬时密度和湍动能的分布和发展。数值模拟获得的界面演化图像和流场中波系结构与实验结果吻合较好。三维和二维模拟结果的比较显示,两者得到的扰动界面位置、波系及湍流混合区边界基本一致,只是后期的界面构型有所不同,这也正说明湍流具有强三维效应。     

流体界面稳定性的线化分析及其对界面实际稳定性的预报

本文用边界积分方法导出了多孔介质中流体界面的发展方程,用线化方法导出了界面的稳定性准则,并通过数值实验研究了线化结果对界面实际稳定性的可预报性。     

不可压结构聚合运动耦合增长的瑞利-泰勒不稳定性研究

推导并计算了不可压圆筒结构的扰动增长方程及具有弹性的运动方程 ,讨论了氧气 乙炔混合气体聚爆明胶圆筒的耦合扰动增长规律 ,研究结果为会聚结构的瑞利 泰勒不稳定性实验提供了很好的理论依据。     

球壳结构馈通增长的瑞利-泰勒不稳定性

利用小扰动分析法 ,导出不可压缩球壳结构的馈通增长方程 ,数值模拟了高压气体驱动外表面有初始扰动的明胶球壳的瑞利 泰勒不稳定性模型。计算结果表明 :对于低波数扰动 ,外界面比较稳定 ,内表面的馈通增长较快 ,具有比较明显的三个演化阶段和波形反转现象。高波数扰动的增长恰好与低波数相反。球壳会聚结构比柱壳会聚结构的界面稳定性要好些。     

Gravity waves and Rayleigh Taylor instability on a Jeffrey-fluid

A theory for linear surface gravity waves on a semi-infinite layer of viscoelastic fluid described by a Jeffrey model is presented. Results are given for the decay rate and the phase velocity as a function of the parameters of the fluid: a nondimensional time constant, and a ratio of the retardation time to the relaxation time. At small wave numbers the behavior is Newtonian. In other cases depending on the nondimensional parameters, a number of possible other behaviors exist. The influence of the non-dimensional parameters on the growth rate of Rayleigh-Taylor instability is also discussed.     

Ablative Rayleigh–Taylor instability in the limit of an infinitely large density ratio

The instability of ablation fronts strongly accelerated toward the dense medium under the conditions of inertial confinement fusion (ICF) is addressed in the limit of an infinitely large density ratio. The analysis serves to demonstrate that the flow is irrotational to first order, reducing the nonlinear analysis to solve a two-potential flows problem. Vorticity appears at the following orders in the perturbation analysis. This result simplifies greatly the analysis. The possibility for using boundary integral methods opens new perspectives in the nonlinear theory of the ablative RT instability in ICF. A few examples are given at the end of the Note. To cite this article: P. Clavin, C. Almarcha, C. R. Mecanique 333 (2005).     

Rayleigh-Taylor instability of an interface in a nonwettable porous medium

The diffusion of vapor through the roof of an underground structure located beneath an aquifer is considered. In the process of evaporation, an interface between the upper water-saturated layer and the lower layer containing an air-vapor mixture is formed. A mathematical model of the evaporation process is proposed and a solution of the steady-state problem is found. It is shown that in the presence of capillary forces in the case of a nonwettable medium the solution is not unique. Using the normal mode method, it is shown that Rayleigh-Taylor instability of the interface can develop in the nonwettable porous medium. It is found that there are two scenarios of loss of stability corresponding to the occurrence of the most unstable wavenumber at zero and at infinity, respectively. It is shown that for zero wavenumber the stability limit is reached at the same time as the solution of the steady-state problem disappears.     

Non-linear study of electrohydrodynamic Rayleigh-Taylor instability in a composite fluid-porous layer

The non-linear electrohydrodynamic RTI in presence of electric field bounded above by porous layer and below by a rigid surface, have been studied based on electrohydrodynamic approximations in the effect similar to the Stokes and lubrication approximations. The non-linear problem is studied numerically in the present paper using the Adams-Bashforth predictor and Adams-Moulton corrector numerical techniques. In the conclusion, the non-linear problem discussed here is quite different from that of Babchin et al. (1983) [10] considering the plane Couette flow. The present problem is greatly influenced by the slip velocity at the interface between porous layer and thin film. It is not amenable to analytical treatment as that of Babchin et al. [10]. Therefore, numerical solutions have to be found. Fourth-order accurate central differences are used for spatial discretization using predictor and corrector numerical technique.     

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Rayleigh-Taylor (R-T) instability is known as the fundamental mechanism of equatorial plasma bubbles (EPBs). However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows: if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments are designed to validate the sufficient conditions. The results agree with the derived sufficient conditions.