当激波与存在初始扰动的物质界面相互作用时，由于压力梯度的方向与密度梯度的方向不重合，致使在扰动界面上沉积斜压涡量，进而诱发 Richtmyer-Meshkov 不稳定性，界面上的扰动经历线性增长、非线性增长， 并在后期导致湍流混合。Richtmyer-Meshkov 不稳定性是一种非常常见的流动现象，从小尺度的惯性约束聚变，到常规尺度的超声速燃烧，再到超大尺度的超新星爆炸，Richtmyer-Meshkov 不稳定性都起着非常重要的作用。目前，世界各国都在积极地开发新的高效洁净能源，利用惯性约束核聚变原理发展核电站是人类未来最理想的能量利用方式。然而，Richtmyer-Meshkov 不稳定性会影响靶丸的压缩和中心处热斑的形成，造成点火失败。因此对 Richtmyer-Meshkov 不稳定性进行研究具有重要意义。本论文针对汇聚（球形和柱形） Richtmyer-Mechkov 不稳定性诱导的湍流混合的流动机理开展数值研究，主要工作包括：

（1）在常规条件下（理想气体，两组分），对球形和柱形汇聚 Richtmyer-Meshkov 不稳定性进行高分辨率隐式大涡模拟数值仿真，以研究几何效应对混合层发展及后期湍流混合特性的影响。主计算区域网格点数达到 2048^3。其中，轻流体是氮气，重流体是六氟化硫，激波马赫数为 1.5，激波从重流体向轻流体汇聚。我们详细对比了球形和柱形汇聚几何情况下，六氟化硫质量分数、 Taylor 微尺度及 Taylor 雷诺数、径向速度脉动均方根、有效 Atwood 数、湍流质量通量速度、密度自相关系数、雷诺应力及其各向异性、脉动谱、湍动能及拟涡能输运特性等湍流混合相关量的分布情况，并进行了条件统计分析。数值模拟结果表明，球形混合层的线性增长率大于柱形混合层，球形混合层内组分之间混合得更加充分。由于球形几何向外扩张效应，球形混合层内气泡高度出现一个明显的快速增长阶段。在质量分数空间，柱形混合层内湍流强度更大。湍动能和拟涡能后期呈现出幂指数衰减规律。球形和柱形混合层后期湍流衰减的主要机制为湍流扩散和耗散。球形和柱形混合层的发展，早期是由斜压项主导的，后期由涡拉伸项主导，可压缩项在前期为正，促进拟涡能产生，后期为负抑制拟涡能产生。

（2）突破常规条件限制，对化学反应柱形汇聚 Richtmyer-Meshkov 不稳定性进行直接数值模拟，以研究化学反应对混合层发展及后期湍流混合特性的影响。其中，轻流体是体积分数为 85% 的氢气和 15% 的氮气，重流体是空气（21% 的氧气和 79% 的氮气），激波马赫数为 1.5，激波从重流体向轻流体汇聚。研究发现，混合层发展的前期，主要是 Richtmyer-Meshkov 不稳定性占据优势，化学反应影响很小，激波二次作用界面之后，混合层迅速发展，组分之间混合程度加剧，化学反应逐渐发挥重要作用。我们对混合层宽度的定义方法进行了讨论，发现化学反应情况下，混合层宽度会增大，并认为混合层内巨大的温度梯度可能是化学反应情况下混合层增大的重要原因。另外，我们将 Youngs 定义的分子混合分数进行推广，以适用于化学反应情况，发现化学反应发生后，混合层内组分之间混合程度减弱。化学反应也会造成流体的膨胀效应增强，压缩效应减弱。

The Richtmyer-Meshkov instability will occur, if a shock wave passes through a perturbed interface between different materials. The main cause that induces Richtmyer-Meshkov instability is baroclinic instability, which will result in the deposition of baroclinic vorticity on the perturbed interface. Under the action of baroclinic vorticity, the amplitude of perturbation experiences linear and nonlinear growth, and then leads to turbulent mixing. The Richtmyer-Meshkov instability is very important in nature and many practical engineering applications, such as inertial confinement fusion (ICF), supersonic combustion and supernova explosion. Nowadays, all countries in the world are actively developing new efficient and clean energy. The development of nuclear power plant based on inertial confinement fusion principle is the most ideal way to utilize energy in the future. However, Richtmyer-Meshkov instability can affect the compression of the target pellet and the formation of hot spots at the center position, and results in ignition failure. Therefore, it is of great significance to study RMI. In this paper, the flow mechanism of turbulent mixing induced by converging Richtmyer-Mechkov instability is studied by numerical simulations. Therefore, the main work of this paper includes:

(1) The Richtmyer-Meshkov instability in spherical and cylindrical converging geometries are simulated by using the high resolution implicit large eddy simulation (ILES) method under an conventional condition (ideal gas, two species), and the influences of geometric effect on the growth of mixing layer width and the characteristics of turbulent mixing are investigated. The total structured and uniform Cartesian grid node number in the main computational domain is 2048^3. The heavy fluid is sulfur hexafluoride, and the light fluid is nitrogen. The shock wave with a Mach number of approximately 1.5 converges from the heavy fluid into the light fluid. We compare the radial distributions or time evolutions of mass fraction of sulfur hexafluoride, Taylor scale and Taylor Reynolds number, root mean square of radial velocity, efficiency Atwood number, turbulent mass-flux velocity, density self-correlation, Reynolds stresses and Reynolds stress anisotropy tensor, spectrum, and turbulent kinetic energy and enstrophy transport equations in spherical and cylindrical converging geometries in detail. In addition, we also conduct conditional statistical analysis. The numerical results show that the linear growth rate of the spherical mixing layer is greater than that of the cylindrical mixing layer, and the mixing between species in the spherical mixing layer is more sufficient. Because of the geometric divergence effect outward, the bubble height has a rapid growth stage in spherical mixing layer. In the mass fraction space, the turbulent intensity is stronger in the cylindrical mixing layer. At the later stage, the turbulent kinetic energy and enstrophy meet the power-law decay of time. The turbulent diffusion and dissipation are the main mechanisms of turbulence decaying at the later stage of mixing layer. The development of spherical and cylindrical mixing layers are dominated by baroclinicity term at the early stage, and by vortex stretching terms at the later stage. The compressibility term is positive at the early stage, which promotes the generation of enstrophy. And it is negative at the later stage, inhibiting the generation of enstrophy.

(2) Breaking through the limitation of conventional conditions, the reactive cylindrical converging Richtmyer-Meshkov is simulated by using the direct numerical simulation method. The main purpose is to study the influence of chemical reaction on the development of mixing layer and turbulent mixing characteristics. The total structured and uniform Cartesian grid node number in the main computational domain is 1024^3. The light fluid is hydrogen with a volume fraction of 85% and nitrogen with a volume fraction of 15%, and the heavy fluid is air (21% oxygen and 79% nitrogen in volume). The shock wave with a Mach number of approximately 1.5 converges from the heavy fluid into the light fluid. It is found that at the early stage of the mixing layer development, the Richtmyer-Meshkov is dominant, and the chemical reaction has little influence. After the reflected shock wave passes through the interface, the mixing layer develops rapidly, the degree of mixing between species intensifies, and the chemical reaction gradually plays an important role. The definition method of mixing layer width is discussed. It is found that the mixing layer width will increase in the case of chemical reaction. The large temperature gradient in the mixing layer may be the important reason for the increase of mixing layer width in the case of chemical reaction. In addition, we generalize the molecular mixing fraction defined by Youngs to apply to chemical reaction case, and found that the mixing degree between species in the mixing layer is weakened for chemical reaction case. Chemical reaction can also increase the expansion effect of the fluid and weaken the compression effect.