作为湍流转捩的驱动力，占据流的统计主导空间状态的趋势
Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition
摘要：
在大雷诺数下发生的从层流到湍流的流体运动的转变通常与层流的不稳定性有关。另一方面，由于湍流特征性地以空间局部结构的形式出现（例如，涡流）填充流场，占据流的这种结构化状态的趋势不能被排除为湍流转变的驱动力。为了研究这种可能性，我们提出了一个简单的分析模型，将流视为局部空间结构的集合，每个结构由基本单元组成，其中粒子（原子或分子）的行为是不相关的。这使我们能够引入雷诺数，将其与系统的总相体积和基本单元的总相体积之间的比率相关联。利用最大熵原理计算了局域结构的最可几尺寸分布，结果表明，随着雷诺数的增加，基本胞团逐渐形成局域结构，从而成功地解释了湍流转捩和湍流的一些一般性质。我们表明，该模型的基本假设，即粒子是不可区分的和基本体积的相空间中存在的粒子的状态是不确定的，参与推导的纳维-斯托克斯方程。考虑到该模型捕捉了湍流的基本特征，这表明湍流转变的驱动力与本模型基本相同，即系统占据统计主导状态的趋势起着关键作用。在高雷诺数下流动的不稳定性可以是启动流动的结构重排以找到该状态的机制。
英文摘要：
The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. We show that the basic assumptions underlying the model, i.e. that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e. the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of the flow to find this state.
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