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.
Acoustical Physics – Springer Journals
Published: Mar 10, 2021