Hydrodynamic moiré superlattice.

The structural periodicity in photonic crystals guarantees the crystal's effective energy band structure, which is the fundamental cornerstone of topological and moiré physics. However, the shear modulus in most fluids is close to zero, which makes it challenging for fluids to maintain spatial periodicity akin to photonic crystals. We realized periodic vortices in hydrodynamic metamaterials and created a bilayer moiré superlattice by stacking and twisting two such vortex fluids. We observed energy delocalization and localization when the twist angles, respectively, result in the Pythagorean and non-Pythagorean triples in the fluidic moiré superlattice. Anomalous localization was found even in commensurate moiré fluids with large lattice constants that satisfy Pythagorean triples. Our work reports the moiré phenomena in fluids and opens an unexpected door to controlling the energy transfer, mass transport, and particle navigation through the elaborate dynamics of vortices in fluidic moiré superlattices.