Low Reynolds number laboratory and numerical simulations of high Reynolds number turbulent mixing

湍流可能看起来是随机的，但我们现在知道，在它的随机性中嵌入了许多秩序和相干/持久的流动结构。湍流还包括许多不同大小的漩涡，在每个尺度上都有随机和连贯/持续的行为。由于这种多尺度结构的混乱和持久的秩序的混合，湍流是很好的混合器。然而，它们消耗大量的能量来维持。层流需要较少的能量消耗。这项研究的目的是双重的。首先，创建和控制新的流动类别，这些流动是层流的，但具有涡内涡的多尺度流动结构。设计新的高效混合器的潜在优势是巨大的。其次，了解多尺度涡旋结构及其相干和随机成分对搅拌和混合的影响。这样的理解从未被尝试过，因为很难将其建立在湍流的实验室实验上，在湍流实验中，监测（更不用说控制）湍流涡流结构，同时测量所得搅拌和混合的统计数据和性质实际上是不可能的。相反，我们建议创建完全双曲型多尺度定制的类似于流的控制多尺度拓扑结构（其特征在于双曲和椭圆停滞点和分形维数）和控制的时间依赖性的流量。通过这种定制流在空间和时间上的多尺度控制，可以研究类顺时针流结构的各个要素之间的关系（多尺度流线拓扑、时间依赖性、强加的随机性和持久性等）以及流的各种统计和性质（例如，在每个尺度下有多少能量，即能谱）以及它们的搅拌和混合特性（例如，混合速率、相邻流体元素的分离速率等）。在随后的阶段，这种详细的时空拓扑了解这些完全控制的定制实验室流将provide的概念工具和框架，以及必要的知识类型，以获得湍流混合模型的基础上，湍流的实际持续拓扑结构及其时间依赖性。到目前为止，湍流混合模型实际上假设湍流只不过是一个随机混合器，而这种模型是有根本性缺陷的。

Turbulence may appear random but we now know that there is much orderand coherent/persistent flow structure embedded in its randomness. Turbulence also consists of eddies of many different sizes with a mix of random and coherent/persistent behaviour at each scale. As a result of this multi-scale structure with its mix of disorder and persistent order, turbulent flows are good mixers. However, they consume a lot of energy to be maintained. Laminar flows require less energy consumotion. The purpose of this research is twofold. Firstly, to create and control new classes of flows which are laminar yet with multi-scale flow structure of eddies within eddies. The potential advantages for the design of new effiicient mixers is enormous. Secondly, to understand how the multi-scale eddying structure and its coherent and random components impact on stirring and mixing. Such an understanding has never been attempted as it is very difficult to ground it on laboratory experiments of turbulent flows where monitoring,let alone controlling, the turbulent eddy structure whilst, at the same time, measuring statistics and properties of the resulting stirring and mixing is virtuallly impossible. Instead, we propose to create fully controllled multi-scale bespoke turbulent-like flows with controlled multi-scale topologies (characterised in terms of hyperbolic and elliptic stagnation points and fractal dimensions) and controlled time-dependencies of the flows. With such multi-scale control in space and time of such bespoke flows, it is then possible to study the relations between the various elements of the turbulent-like flow structure (multi-scale streamline topology, time dependence, imposed randomness and persistence, etc) and the various statistics and properties of the flows (e.g. how much energy at each scale, i.e energy spectra) and of their stirring and mixing proporties (e.g. mixing rates, rate of separation of neighboring fluid elements, etc). At a subsequent stage, such detailed spatio-temporal topological understanding of these fully controlled bespoke laboratory flows will procvide the conceptual tools and framework and the type of knowledge necessary to derive models of turbulent mixing based on the actual persistent topology of the turbulence and its time dependence. Turbulent mixing models to this date effectively assume the turbulence to be no more than just a random mixer, and such models are known to be fundamentally flawed.