The surprising fate of turbulence in fluids with odd viscosity

Turbulent flows can be altered in very far-reaching ways by the presence of non-dissipative components in the viscosity tensor of the fluid. Such viscosity, called odd, Hall- or gyro-viscosity, can emerge in chiral systems ranging from plasma and bio-active media to quantum fluids. Using a combination of theory and direct numerical simulations in 3D, we show that odd viscosity yields a tendency to invert the direction of the turbulent energy cascade. This results in an intermediate range of scales of the flow in which kinetic energy condensates, producing a well-defined pattern in the flow. The flow statistics in this condensate range are entirely different from conventional turbulent flows, being fully self-similar and non-intermittent. At yet smaller scales, when odd viscosity becomes even more dominant, we show that we can enter a regime dominated by wave-turbulence as evidenced from spatio-temporal energy spectra and theoretical arguments. Finally, we discuss how to pave the way towards making an odd viscous fluid in the lab.