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. 
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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/

[1] A. Boudlal and V. Yu. Liapidevskii, “Roll waves in channels with an active gas phase”, J. Appl. Mech. Tech. Phys., 56:4 (2015), 541–548 | DOI | MR | Zbl

[2] Boutounet M., Noble P., Vila J.-P., “Roll-waves in bi-layer flows”, Math. Models Methods Appl. Sci., 22:6 (2012), 1250006 | DOI | MR

[3] Chesnokov A., “Formation and evolution of roll waves in a shallow free surface flow of a power-law fluid down an inclined plane”, Wave Motion, 106 (2021), 102799 | DOI | MR

[4] A. A. Chesnokov and V. Yu. Liapidevskii, “Roll wave structure in long tubes with compliant walls”, Proc. Steklov Inst. Math., 300 (2018), 196–205 | DOI | DOI | MR | Zbl

[5] Chesnokov A., Liapidevskii V., Stepanova I., “Roll waves structure in two-layer Hele–Shaw flows”, Wave Motion, 73 (2017), 1–10 | DOI | MR

[6] V. A. Davydov, V. S. Zykov, and A. S. Mikhailov, “Kinematics of autowave structures in excitable media”, Phys. Usp., 34:8 (1991), 664–684 | DOI

[7] Dressler R.F., “Mathematical solution of the problem of roll-waves in inclined open channels”, Commun. Pure Appl. Math., 2:2–3 (1949), 149–194 | DOI | MR | Zbl

[8] Field G.B., “Thermal instability”, Astrophys. J., 142:2 (1965), 531–567 | DOI

[9] Johnson M.A., Zumbrun K., Noble P., “Nonlinear stability of viscous roll waves”, SIAM J. Math. Anal., 43:2 (2011), 577–611 | DOI | MR | Zbl

[10] Krasnobaev K.V., Tagirova R.R., “Isentropic thermal instability in atomic surface layers of photodissociation regions”, Mon. Not. R. Astron. Soc., 469:2 (2017), 1403–1413 | DOI

[11] K. V. Krasnobaev and R. R. Tagirova, “Influence of a magnetic field on wave motions in thermally unstable photodissociation regions”, Astron. Lett., 45:3 (2019), 147–155 | DOI | DOI

[12] K. V. Krasnobaev, R. R. Tagirova, S. I. Arafailov, and G. Yu. Kotova, “Evolution and saturation of autowaves in photodissociation regions”, Astron. Lett., 42:7 (2016), 460–473 | DOI | DOI

[13] A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems, Chapman Hall/CRC, Boca Raton, FL, 2001 | MR | Zbl

[14] V. Yu. Liapidevskii, “Roll waves in a gas–liquid medium”, J. Appl. Mech. Tech. Phys., 43:2 (2002), 204–207 | DOI | MR | Zbl

[15] Lyapidevskii V.Yu., Teshukov V.M., Matematicheskie modeli rasprostraneniya dlinnykh voln v neodnorodnoi zhidkosti, Izd-vo SO RAN, Novosibirsk, 2000

[16] Molevich N., Riashchikov D., “Shock wave structures in an isentropically unstable heat-releasing gas”, Phys. Fluids, 33:7 (2021), 076110 | DOI

[17] Molevich N.E., Zavershinsky D.I., Galimov R.N., Makaryan V.G., “Traveling self-sustained structures in interstellar clouds with the isentropic instability”, Astrophys. Space Sci., 334:1 (2011), 35–44 | DOI | Zbl

[18] Nessyahy H., Tadmor E., “Non-oscillatory central differencing for hyperbolic conservation laws”, J. Comput. Phys., 87:2 (1990), 408–463 | DOI | MR

[19] G. B. Whitham, Linear and Nonlinear Waves, J. Wiley Sons, New York, 1974 | MR | Zbl

[20] Zavershinskiy D.I., Molevich N.E., Ryashchikov D.S., “Structure of acoustic perturbations in heat-releasing medium”, Procedia Eng., 106 (2015), 363–367 | DOI