过渡河道水流：一个最小随机模型
Transitional channel flow: A minimal stochastic model
摘要：
在与Pomeau的猜想有关的定向渗流（DP）的湍流的发生/衰减在壁有界的流动，我们提出了一个最小的随机模型，致力于解释的空间间歇性制度观察到的通道流之前，它返回到层流。数值模拟表明，一个政权与带倾斜漂移在两个流向对称的方向分叉成一个不对称的制度，最终衰减到层流。该模型表示在一个概率元胞自动机进化冯诺依曼邻域的概率推导出一个密切的检查模拟结果。它实现了带传播和两个主要的局部过程：纵向分裂涉及具有相同方向的带，横向分裂产生一个与其母亲方向相反的子带。观察到的最终衰减阶段显示一维DP属性在一个二维的几何形状被解释为导致在单一取向制度的横向扩展的无关性。该模型还再现了分叉恢复对称性的概率附加到横向分裂，这开辟了道路，该分叉的临界特性的研究，在类似于热力学相变的变化。
英文摘要：
In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton evolving von Neumann neighbourhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.
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