Abstract

The paper proposes to describe the dynamics of perturbations of compressible ideal gas flows in the formalism of Lagrangian mechanics. The key point is the choice of generalized coordinates that most naturally describe the system dynamics. The proposed choice of main variables leads to the Lagrange equations, which correspond to the displacement field equation and convective wave equation for the scalar potential. This approach yields the acoustic energy balance equation via the first variations of the variables for the flows with nonzero vorticity. The results can be used for energy analysis of the sound emission for flows with localized vortices, jet flows, and duct flows.

中文翻译：

---

关于使用拉格朗日力学方法分析压缩气体涡流中的能量平衡

摘要

本文建议以拉格朗日力学的形式主义来描述可压缩理想气流的扰动动力学。关键是选择最自然地描述系统动力学的广义坐标。建议的主要变量选择导致Lagrange方程，该方程对应于标量势的位移场方程和对流波方程。该方法通过具有非零涡度的流动的变量的第一变化产生声能平衡方程。该结果可用于对具有局部涡流，射流和管道流的流的声发射进行能量分析。