Abstract

Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where the cascade is eventually arrested by dissipation. In this talk, we will discuss how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which in its simplest incarnation can be traced to the linear instability of a homogeneous state. By contrast, the mechanism we propose here is fully non-linear. It is triggered by a 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. 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 bio-active to quantum systems. Beyond fluids with odd viscosity, we will discuss how cascade-induced patterns may also arise in other structured fluids as well as in contexts such as pulverization where mass rather than energy cascades.