Archives of Acoustics, 44, 3, pp. 551–559, 2019

Nonlinear Interaction of Modes in a Planar Flow of a Gas with Viscous and Thermal Attenuation

Technical University of Gdansk

The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.
Keywords: nonlinear wave theory; nonlinear acoustics; coupling dynamic equations; Burgers equation; diffusion equation
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DOI: 10.24425/aoa.2019.129270