Pattern formation by turbulent cascades

• Published in: Nature (London) 2024-03, Vol.627 (8004), p.515-521
• Main Authors: de Wit, Xander M., Fruchart, Michel, Khain, Tali, Toschi, Federico, Vitelli, Vincenzo
• Format: Article
• Language: English
• Subjects: 639/766; 639/766/189; 639/766/530; Arrests; Blood Coagulation; Coagulation; Dissipation; Energy; Feces; Fluid flow; Humanities and Social Sciences; Law Enforcement; multidisciplinary; Navier-Stokes equations; Pattern formation; Plasma; Rotating fluids; Science; Science (multidisciplinary); Transport properties; Turbulence; Viscosity; Vortices; Wavelength
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/s41586-024-07074-z

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 – 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 state 7 . 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 – 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 scales 4 . Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows 13 – 19 , stellar plasma such as the solar wind 20 – 22 , or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades 23 – 25 . Turbulent energy cascades can be arrested by non-dissipative viscosities, resulting in pattern formation at intermediate length scales.