  Two common concepts of nonreciprocity in sound propagation are based on
nonlinear effects [1, 2] and on local circulation of fluid [3, 4]. They
originate from two known methods of breaking a time reversal symmetry, that is
necessary for observation of nonreciprocal effects. Both concepts require
additional devices to be installed with their own power sources. Recently it
was demonstrated that acoustical losses may serve as a source of T-symmetry
violation, thus leading to nonreciprocity in reflection of sound from
gradient-index metasurface [5]. Here, we explore viscosity of fluid as a
natural factor of T-symmetry breaking. We report experimental observation of
the nonreciprocal transmission of ultrasound through a water-submerged phononic
crystal consisting of asymmetric rods. Asymmetry, or broken P-symmetry, is the
second necessary factor for nonreciprocity. Experimental results are in
agreement with numerical simulations based on the Navier-Stokes equation. This
passive nonreciprocal linear device is cheap, robust and does not require an
energy source.
