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**On a general theory for compressing process and aeroacoustics: linear analysis.**
*(English)*
Zbl 1269.76108

Summary: Of the three mutually coupled fundamental processes (shearing, compressing, and thermal) in a general fluid motion, only the general formulation for the compressing process and a subprocess of it, the subject of aeroacoustics, as well as their physical coupling with shearing and thermal processes, have so far not reached a consensus. This situation has caused difficulties for various in-depth complex multiprocess flow diagnosis, optimal configuration design, and flow/noise control. As the first step toward the desired formulation in fully nonlinear regime, this paper employs the operator factorization method to revisit the analytic linear theories of the fundamental processes and their decomposition, especially the further splitting of compressing process into acoustic and entropy modes, developed in 1940s–1980s. The flow treated here is small disturbances of a compressible, viscous, and heat-conducting polytropic gas in an unbounded domain with arbitrary source of mass, external body force, and heat addition. Previous results are thereby revised and extended to a complete and unified theory. The theory provides a necessary basis and valuable guidance for developing corresponding nonlinear theory by clarifying certain basic issues, such as the proper choice of characteristic variables of compressing process and the feature of their governing equations.

### MSC:

76Q05 | Hydro- and aero-acoustics |

### Keywords:

longitudinal (compressing) process; transversal (shearing) process; acoustic mode; entropy mode; aeroacoustics
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\textit{F. Mao} et al., Acta Mech. Sin. 26, No. 3, 355--364 (2010; Zbl 1269.76108)

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