AI 中文总结
该研究构建声学类比的输运几何，明确其源重归因的和乐性，揭示近似源模型输运会产生无参数远场偏差，结果经符号与数值验证。
AI 中文摘要
声学类比的源项并非唯一：对纳维-斯托克斯方程的不同重新排列，会将相同的辐射声归因于不同的表观源。尽管这种非唯一性早已被认识到，但从未被赋予定量结构。我们通过将声学类比组织为有效介质空间上的类纤维族，并通过唯一的保频率、无旋的线性时空映射定义类比间的输运，提供了这样一种结构。由此得到三个完整结果：第一，经典的对流类比族在输运下不闭合：连续的均匀流重定标会生成具有各向异性声速张量的有效介质，从而恢复Goldstein引入的广义介质。第二，类比输运的离散和乐性以闭式形式得到，它由一个完整的谱膨胀和一个在马赫数四阶时消失的旋转构成；输运在类比空间的声视界上变为奇异。第三，在连续极限下， boost 扇区是平坦的，而曲率被限制在各向异性方向，且由声速张量增量的对易子给出。该几何并不意味着物理声场的任何改变：所有完整类比都产生相同的远场。其意义在于操作性：当近似源模型在类比间输运时（这在混合预测方法中很常见），所得的远场预测会获得一种完整的、无参数的偏差，由刚性谱膨胀和指向旋转构成。各向异性介质的完整远场定律将这些结果扩展到开放输运路径，所有恒等式均通过符号和数值验证。
英文摘要
The source term of an acoustic analogy is not unique: different rearrangements of the Navier-Stokes equations attribute the same radiated sound to different apparent sources. Although this non-uniqueness has long been recognised, it has never been given a quantitative structure. We provide one by organising acoustic analogies into a fibre-like family over the space of effective media and defining transport between analogies through unique frequency-preserving, rotation-free linear space-time maps. Three exact results follow. First, the classical family of convected analogies is not closed under transport: successive uniform-flow regaugings generate effective media with anisotropic sound-speed tensors, recovering the generalised media introduced by Goldstein. Second, the discrete holonomy of analogy transport is obtained in closed form. It consists of an exact spectral dilation and a rotation that vanishes to fourth order in Mach number; transport becomes singular on a sonic horizon in analogy space. Third, in the continuum limit the boost sector is flat, while curvature is confined to anisotropy directions and is given by the commutator of sound-speed-tensor increments. The geometry does not imply any change in the physical sound field: all exact analogies yield the same far field. Its significance is operational. When an approximate source model is transported between analogies, as commonly occurs in hybrid prediction methods, the resulting far-field predictions acquire an exact, parameter-free bias consisting of a rigid spectral dilation and directivity rotation. An exact far-field law for anisotropic media extends these results to open transport paths. All identities are verified symbolically and numerically.
