Geodesic
Wave Structures in Ideal Gas Flows with an External Energy Source
Informatics and Automation, Modern Methods of Mechanics, Tome 322 (2023), pp. 241-250

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We consider the propagation of plane waves in an ideal gas in the presence of external sources of energy inflow and dissipation. Using the Whitham criterion, we obtain conditions under which small perturbations of a constant solution are transformed into nonlinear quasiperiodic wave packets of finite amplitude that move in opposite directions. The structure of these wave packets is shown to be similar to roll waves in inclined open channels. We perform numerical calculations of the development of self-oscillations and the nonlinear interaction of waves. The calculations show that under a small harmonic perturbation of the initial equilibrium state, two types of wave structures can develop: roll waves and periodic two-peak standing waves.
Keywords: hyperbolic equations, ideal gas, thermal instability, roll waves. 
@article{TRSPY_2023_322_a18,
     author = {A. A. Chesnokov},
     title = {Wave {Structures} in {Ideal} {Gas} {Flows} with an {External} {Energy} {Source}},
     journal = {Informatics and Automation},
     pages = {241--250},
     publisher = {mathdoc},
     volume = {322},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2023_322_a18/}
}
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A. A. Chesnokov. Wave Structures in Ideal Gas Flows with an External Energy Source. Informatics and Automation, Modern Methods of Mechanics, Tome 322 (2023), pp. 241-250. http://geodesic.mathdoc.fr/item/TRSPY_2023_322_a18/