A stone falls into a pond, and ripples spread evenly in all directions. But some media behave as if the wave knows which way to turn, like water that only swirls clockwise. This asymmetry comes from odd viscosity and odd elasticity — properties of media with broken mirror symmetry. They appear, for instance, in certain liquid crystals or in active fluids made of living cells.
The authors built a theory of turbulence for such media, where many weak random waves interact. For a three-dimensional fluid with odd viscosity, they derived an equation showing how energy flows from large vortices to small ones. This direct cascade follows a special spectrum, the distribution of energy across vortex sizes, that depends on direction. For a one-dimensional elastic thread with odd elasticity, the picture is different. Waves interact much more slowly, and an inverse cascade emerges. Energy gathers into large-scale motions, as if ripples on a rope suddenly merged into one smooth bend.
Computer simulations confirmed both predictions. For odd viscosity, the direct cascade with an anisotropic spectrum is clearly visible. For odd elasticity, the inverse cascade is a bit smeared, the theory points to a logarithmic correction, but still recognizable. These results are not just a mathematical exercise. They help us understand how active media behave, from the cell cytoskeleton to geophysical flows, where symmetry is broken and the usual laws of turbulence fail. So a stone thrown into an unusual pond creates ripples that remember their direction.
Odd viscosity was first described for electrons in a magnetic field: it makes the fluid flow perpendicular to the applied force, as if an invisible conductor is directing the flow.
In Peter Watts's novel Blindsight, alien life uses asymmetric fields and unusual physical principles — media with odd elasticity could be the basis of their biomechanics.