It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes non-reciprocal 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 non-reciprocal contribution to the transmission coefficient. The non-reciprocal transmission spectra for a phononic crystal of metallic circular cylinders in water are experimentally obtained and analysed. 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 non-reciprocal part of transmission is separated from its asymmetric reciprocal part in numerically simulated transmission spectra. The level of non-reciprocity 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 non-reciprocity. It also opens a way for engineering passive acoustic diodes exploring the natural viscosity of any fluid as a factor leading to non-reciprocity.

中文翻译：

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粘性环境中的非互易声学

已经证明，如果背景流体是粘性的，则通过具有各向异性固体散射体的声子晶体的声学传输变得非互易。在理想（无粘性）流体中，沿破坏 P 对称方向的传输是不对称的。这种不对称性与互易性兼容，因为时间反转对称性（T 对称性）成立。粘性损失破坏了 T 对称性，增加了对传输系数的非互易贡献。通过实验获得并分析了水中金属圆柱体声子晶体的非互易透射光谱。圆柱体的表面经过特殊处理，以通过操纵表面特征弱破坏 P 对称性并增加粘性损失。随后，在数值模拟的透射光谱中，透射的非互易部分与其不对称的互易部分分开。非互易程度与破坏 P 对称性的度量一致。报告的研究与普遍接受的观点相矛盾，即线性耗散不能成为导致非互惠的原因。它还为设计无源声学二极管开辟了道路，探索任何流体的自然粘度作为导致非互易性的因素。