AI 中文总结
本文综述了普朗特-格劳厄特-洛伦兹变换所揭示的可压缩势流理论与狭义相对论之间的数学对应关系，并借助附加质量概念表明线性化可压缩势流理论可精确镜像狭义相对论的整个数学框架。
AI 中文摘要
普朗特-格劳厄特-洛伦兹变换建立了可压缩势流理论与狭义相对论之间深刻的数学对应关系。尽管自二十世纪初以来，这一类比在空气动力学文献中已隐含存在，但在两个领域之间仍未得到广泛认识，也从未以统一的方式进行过综述。本综述以两个领域都能理解的自洽且教学化的框架，呈现了这一对应关系的历史、数学和应用维度。在追溯了可压缩空气动力学理论与狭义相对论平行发展的历程之后，我们确立了洛伦兹变换与普朗特-格劳厄特坐标变换之间的形式等价性，并在声学框架内重新诠释了时间膨胀、多普勒效应和洛伦兹因子等相对论概念。借助附加质量概念，我们最终扩展了这一类比，并表明狭义相对论的整个数学框架恰好被线性化可压缩势流理论所镜像。
英文摘要
The Prandtl-Glauert-Lorentz transformation establishes a deep mathematical correspondence between compressible potential flow theory and special relativity. Despite being implicit in the aerodynamic literature since the early twentieth century, this analogy remains largely unrecognised across the two communities and has never been surveyed in a unified manner. This review presents, in a self-contained and pedagogical framework accessible to both communities, the historical, mathematical, and applied dimensions of this correspondence. After tracing the parallel developments that gave rise to compressible aerodynamic theory and special relativity, we establish the formal equivalence between the Lorentz transformation and the Prandtl-Glauert coordinate change, and reinterpret relativistic concepts such as time dilation, the Doppler effect, and the Lorentz factor within the acoustic framework. Thanks to the added mass concept, we finally extend this analogy and show that the whole mathematical framework of special relativity is exactly mirrored by the linearised compressible potential flow theory.
Journal refPhysics of Fluids, 2026, 38 (9), pp.096112
