It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes nonreciprocal if the background fluid is viscous. In an ideal (inviscid) fluid, the transmission along the direction of broken P symmetry is asymmetric. This asymmetry is compatible with reciprocity since time-reversal symmetry (T symmetry) holds. Viscous losses break T symmetry, adding a nonreciprocal contribution to the transmission coefficient. The nonreciprocal transmission spectra for a phononic crystal of metallic circular cylinders in water are experimentally obtained and analyzed. The surfaces of the cylinders were specially processed in order to weakly break P symmetry and increase viscous losses through manipulation of surface features. Subsequently, the nonreciprocal part of transmission is separated from its asymmetric reciprocal part in numerically simulated transmission spectra. The level of nonreciprocity is in agreement with the measure of broken P symmetry. The reported study contradicts commonly accepted opinion that linear dissipation cannot be a reason leading to nonreciprocity. It also opens a way for engineering passive acoustic diodes exploring natural viscosity of any fluid as a factor leading to nonreciprocity.

The transmission spectra for the experiments were measured using a thru-transmission setup. The detail information is written in the manuscript. The data was collected using the oscilloscope and processed in Matlab. The dissipated energy was calculated through the numerical simulation using COMSOL multiphysics and processed in Matlab.