从有向渗流到图案化湍流
From directed percolation to patterned turbulence
AI总结：
本研究针对湍流转捩中条纹图案的形成机制问题，发现图案并非源于经典不稳定性的波长选择，而是从有向渗流临界点出发、由局部随机规则自组装形成，揭示了随机过程中宏观有序性的新产生机制。
摘要：
向湍流的转捩以有序性和可预测性的骤然丧失为特征，表现为局地湍流结构的间歇性增殖与衰减。在流动发展为完全湍流的过程中，令人意外的是，当交替的层流与湍流区域排列成规则的条纹图案时，有序性会重新出现。此前人们认为，这种宏观组织是自上而下由湍流的经典图案形成不稳定性产生的，会给无序流场印刻上一个特征波长。而我们在此证明，图案反而是随流速升高自组装形成的。从间歇性条纹区出发，具体而言从对应的有向渗流（directed percolation, DP）临界点出发，规则图案会在DP转捩的标度范围内形成。同样地，图案的扩展速率由DP临界指数决定，这证明所有底层过程都是随机的。通过摒弃层流与湍流是对立状态的普遍认知，这种内在随机性与所呈现有序性之间的明显矛盾得到了解决。更广泛地说，我们的研究例证了：在不存在通常与图案形成相关的波长选择机制的情况下，宏观图案可以仅由局部随机规则产生。
英文摘要：
The transition to turbulence is characterized by an abrupt loss of order and predictability, featuring the intermittent proliferation and decay of localized turbulent structures. En-route to becoming fully turbulent, surprisingly order reappears when alternating laminar and turbulent regions arrange in regular stripe patterns. This macroscopic organization is believed to arise top down from a classic pattern forming instability of turbulence, imprinting a wavelength onto the disordered flow field. We here demonstrate that patterns instead self-assemble with increasing velocity. Starting from the intermittent stripe regime, specifically from the corresponding directed percolation (DP) critical point, regular patterns are established within the scaling range of the DP transition. Likewise the patterns' expansion rates are set by the DP critical exponents, attesting that all underlying processes are stochastic. This apparent contradiction between the inherent stochasticity and the displayed order is resolved by abandoning the common perception of laminar and turbulence as opposing states. More generally our study exemplifies that macroscopic patterns can arise solely from local stochastic rules, in the absence of wavelength selection typically associated with pattern formation.
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