Active fluids display collective phenomena such as active turbulence or odd viscosity, which refer to spontaneous complex and transverse flow. The simultaneous emergence of these seemingly separate phenomena is here reported in experiment for a chiral active fluid composed of a carpet of standing and spinning colloidal rods, and in simulations for synchronously rotating hard discs in a hydrodynamic explicit solvent. Experiments and simulations reveal that multi-scale eddies emerge, a hallmark of active turbulence, with a power-law decay of the kinetic-energy spectrum, a feature of self-similar dynamics. Moreover, the particles are dragged to the centre of the vortices, a telltale sign of odd viscosity. The weak compressibility of the system enables an explicit measurement of the odd viscosity in bulk via the relation between local vorticity and excess density. Our findings are relevant for the understanding of biological systems and for the design of microrobots with collective self-organized behavior.
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