Nonreciprocity of acoustic intensity in viscous fluids

A mechanism of nonreciprocal transmission of sound through a viscous environment with asymmetric scatterers is proposed and experimentally demonstrated using a Tesla valve filled by stationary liquids with different viscosities. The nonreciprocal quantity is the local intensity of sound. Unlike pressure, which remains reciprocal even in a viscous fluid, the intensity exhibits nonreciprocity due to the asymmetry of the field of acoustic velocities if the mirror symmetry ($P$ symmetry) is broken by asymmetric scatterers. Nonreciprocity in intensity appears in the linear regime of propagation, while the intensity itself scales quadratically with the amplitude of sound. Our study supports the general conclusion that Newton's dynamics of a system with broken time-reversal symmetry ($T$ symmetry) is nonreciprocal. Due to the irreversibility of viscous fluid dynamics, the dissipation-induced nonreciprocity does not follow Onsager symmetry, unlike nonreciprocity caused by fluid motion or magnetic field.