  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 article, 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 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. 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 bio-active 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 where a two-dimensionalization occurs at large
scales. Beyond 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
where mass rather than energy cascades.
