近日，荷兰埃因霍温科技大学的Federico Toschi及其研究小组与芝加哥大学的Vincenzo Vitelli等人合作并取得一项新进展。经过不懈努力，他们通过湍流级联形成图案。相关研究成果已于2024年3月20日在国际权威学术期刊《自然》上发表。

该研究团队展示了如何利用这些看似无结构的湍流级联来生成图案。图案的形成需要一个波长选择的过程，这通常可以追溯到均匀状态的线性不稳定性。相反，该研究提出的机制是完全非线性的。它是由湍流级联的非耗散停止触发的: 能量在中间尺度堆积，这既不是系统大小，也不是能量通常耗散的最小尺度。他们利用理论和大规模模拟的结合，表明这些级联诱导图案的可调波长可以通过称为奇粘度的非耗散输运系数来设置，奇粘度在从生物活性到量子系统的手性流体中普遍存在。

奇粘度作为一种依赖于尺度的类科里奥利力，在小尺度上导致流动的二维化，与旋转流体在大尺度上发生二维化形成对比。除了奇粘度流体之外，研究人员还讨论了级联诱导图案如何在自然系统中出现，包括大气流动，恒星等离子体(如太阳风)，或质量而不是能量级联的物体或液滴的粉碎和凝固。

据悉，充分发展的湍流是一种普遍的、尺度不变的混沌状态，其特征是从大尺度到小尺度的能量级联，在小尺度上，能量级联最终因耗散而停止。

附：英文原文

Title: Pattern formation by turbulent cascades

Author: de Wit, Xander M., Fruchart, Michel, Khain, Tali, Toschi, Federico, Vitelli, Vincenzo

Issue&Volume: 2024-03-20

Abstract: Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows, stellar plasma such as the solar wind, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades.

DOI: 10.1038/s41586-024-07074-z

Source: https://www.nature.com/articles/s41586-024-07074-z