Abstract

Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where it is eventually arrested by dissipation. In this talk, we 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. 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 dissipated. The tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd or gyro viscosity ubiquitous in chiral systems ranging from plasma to bio-active media. Cascade-induced patterns could also occur in natural systems such as atmospheric or astrophysical flows as well as the pulverization of objects or the coagulation of droplets where mass rather than energy cascades. Finally, we discuss how spatial patterns in the distribution of cytoskeletal proteins trigger morphogenetic flows in fruit fly embryos. Using a suite of machine learning techniques we discover a closed-loop dynamical system that controls fruit fly morphogenesis during gastrulation and validate it with a mutant analysis.