High-Schmidt number turbulent mixing as an aggregation process

在许多地球物理、工业、自然或人为应用中，湍流中被动平流物质的混合是一个普遍存在的基本过程。当混合标量浓度的扩散系数小于平流流体的运动粘度时，底层搅拌场运动与最终扩散过程之间的相互作用是非平凡的，即施密特数下的Batchelor状态远大于单位。在这种状态下，浓度场自组织，低于速度场最小涡流的大小，作为一组薄片，随着它们逐渐消失而聚集，从而建立了混合物的浓度含量。在本项目中，我们希望将实验室实验和直接数值模拟相结合，以更详细地探索混合作为聚合过程的愿景，并将其扩展到三维情况。不同的标量源以及不同的施密特数和雷诺数的影响将在实验和模拟中进行系统的研究，在尽可能简单的流动配置中，以解决整个过程的基本问题。目标将是在聚合模型的基础上，对高施密特数黏性对流范围内的标量统计进行完整的描述。

The mixing of passively advected substances in turbulent flows is a fundamental process omnipresent in many geophysical, industrial, natural or man-made applications. The interplay between the motions of the underlying stirring field and the ultimate diffusive process is non-trivial when the diffusivity of the mixed scalar concentration is smaller than the kinematic viscosity of the advecting fluid, the so-called Batchelor regime at Schmidt numbers much larger than unity. In this regime, the concentration field self-organises, below the size of the smallest eddies of the velocity field, as a set of sheets, aggregating as they fade away, thus building up the concentration content of the mixture. In the present project, we want to combine laboratory experiments and direct numerical simulations in order to explore in more details this vision of mixing as an aggregation process, and extend it to the three-dimensional case. The impact of different scalar sources as well as of different Schmidt and Reynolds numbers will be studied systematically, both in experiment and simulation, in flow configurations kept as simple as possible, in order to address the fundamentals of the overall process. The goal will be a complete description of the scalar statistics in the viscous-convective range at high Schmidt numbers on the basis of the aggregation model.