Pattern formation by turbulent cascades

Fully developed turbulence is a universal, scale-invariant chaotic state where energy injected at large scales cascades nonlinearly to smaller scales and is ultimately dissipated. The authors show that such turbulent cascades can generate patterns via a fully nonlinear mechanism triggered by the non-dissipative arrest of the cascade: energy accumulates at an intermediate scale that is neither the system size nor the smallest dissipative scale. Using theory and large-scale simulations, they demonstrate that the tunable wavelength of these cascade-induced patterns can be controlled by a non-dissipative transport coefficient—odd viscosity—ubiquitous in chiral fluids from bioactive to quantum systems. Odd viscosity acts as a scale-dependent Coriolis-like force that two-dimensionalizes the flow at small scales (opposite to rotation, which two-dimensionalizes at large scales). The study further discusses how similar cascade-induced patterns can arise in natural systems, including atmospheric flows, stellar plasmas such as the solar wind, and in mass cascades like droplet coagulation and breakup.

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