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Center for Nonlinear Studies |
Fully developed turbulence is a universal chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation. Here we show how to harness 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 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. 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. We furthermore show that in the regime that is dominated by odd viscosity, the intermittency of turbulence is suppressed, which can be traced back to the broken scale invariance. Finally, we show that even a regime can be entered that is dominated by waves generated by the odd viscosity, giving rise to weak wave turbulence.
Host: Syed Shah