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^1,2,3,4,5,6. 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 state⁷. 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^8,9,10,11,12. 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 scales⁴. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows^{13,14,15,16,17,18,19}, stellar plasma such as the solar wind^20,21,22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades^23,24,25.

完全发展的湍流是一种普遍且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，级联最终被耗散所阻止^1,2,3,4,5,6。在这里，我们展示了如何利用这些看似无结构的湍流级联来生成模式。图案形成需要波长选择的过程，这通常可以追溯到均匀状态⁷的线性不稳定性。相比之下，我们在这里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：能量在中间尺度上堆积，这既不是系统尺寸，也不是能量通常耗散的最小尺度。结合理论和大规模模拟，我们表明这些级联诱导模式的可调波长可以通过称为奇粘度的非耗散传输系数来设置，该系数普遍存在于从生物活性到量子系统的手性流体中^{8,9 ,10,11,12}。奇粘度充当与尺度相关的类科里奥利力，导致小尺度下的流动二维化，这与在大尺度下发生二维化的旋转流体形成鲜明对比⁴。除了奇怪的粘度流体之外，我们还讨论了自然系统中如何出现级联引起的模式，包括大气流^{13,14,15,16,17,18,19}，恒星等离子体，例如太阳风^20,21,22，或物体或液滴的粉碎和凝结，其中质量而不是能量级联^23,24,25。