Noether's theorem reads: ``A symmetry implies a conservation law". From a single relativistic energy equation of fluid motion, two conservation equations are obtained in the non-relativistic limit: mass conservation and energy conservation of traditional form. We are concerned with the mass conservation equation and investigate what symmetry implies the mass conservation, and conversely what symmetry the mass conservation implies. This study is guided by the general representation of rotational flows of an ideal compressible fluid satisfying Euler's equation derived by Kambe in 2013, giving a hint of existence of a set of gauge fields. Thus our physical system is a combined system consisting of a fluid flow and a background field described with a set of gauge fields. The gauge invarinace of the latter fields assures the law of mass conservation. Conversely as far as the mass conservation law is valid, the gauge invariance is assured for the action representing interaction between the two components of the combined fields. The proposed background field has wavy nature. Present combined system describes wave excitation by fluid flows, both irrotational and rotational, and enables rederivation of the Lighhthill's equation of aerodynamic sound with a correction term naturally. Rotational waves are also excited in shear flows with their phase speed different from the sound speed.

中文翻译：

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流体力学中质量守恒定律和波的新观点

后一个域的规范不变性保证了质量守恒定律。相反，只要质量守恒定律有效，表示组合场的两个分量之间相互作用的动作的规范不变性得到保证。建议的背景场具有波浪性质。目前的组合系统描述了由非旋转和旋转流体流动引起的波激发，并且能够自然地用校正项重新推导空气动力学声学的莱特希尔方程。旋转波也在剪切流中被激发，其相位速度与声速不同。建议的背景场具有波浪性质。目前的组合系统描述了由非旋转和旋转流体流动引起的波激发，并且能够自然地用校正项重新推导空气动力学声学的莱特希尔方程。旋转波也在剪切流中被激发，其相位速度与声速不同。建议的背景场具有波浪性质。目前的组合系统描述了由非旋转和旋转流体流动引起的波激发，并且能够自然地用校正项重新推导空气动力学声学的莱特希尔方程。旋转波也在剪切流中被激发，其相位速度与声速不同。