Odd wave turbulence

Abstract

Wave turbulence describes the statistical dynamics of weakly interacting waves in out-of-equilibrium systems. These systems are out of equilibrium because forcing and dissipation occur at different scales, leading to a flux across scales known as a turbulent cascade. However, the underlying medium is usually assumed to be passive. Here, we study situations where a turbulent cascade takes place on top of a driven-dissipative steady-state, which is already out of equilibrium without forcing. We focus on chiral active media, in which waves arise as a consequence of non-reciprocal responses known as odd viscosity and odd elasticity. Combining analytical theory with large-scale direct numerical simulations, we show that fluids with odd viscosity sustain weak wave turbulence down to the smallest active scales, leading to anisotropic Kolmogorov-Zakharov spectra and a modified forward cascade. In the odd elastic solids, two new conserved quantities emerge (which we call wave action and odd energy), giving rise to an inverse cascade in the weak regime and a forward cascade in the strong regime. Our results pave the way towards understanding the chaotic nonlinear regime of systems with nonreciprocal responses from chiral plasma to engineered solids.