Инд. авторы:	Grigoryev Y.N., Ershov I.V.
Заглавие:	Energy theory of nonlinear stability of plane shear flows of thermally nonequilibrium gas
Библ. ссылка:	Grigoryev Y.N., Ershov I.V. Energy theory of nonlinear stability of plane shear flows of thermally nonequilibrium gas // Fluid Mechanics and its Applications. - 2017. - Vol.117. - P.111-151. - ISSN 0926-5112.
Внешние системы:	DOI: 10.1007/978-3-319-55360-3_5; РИНЦ: 29498601; SCOPUS: 2-s2.0-85017449796; WoS: 000424706100007;
Реферат:	eng: The energy stability theory extended by the authors to the case of compressible flows of a vibrationally excited molecular gas is used to study stability of a subsonicCouette flow. Universal approach is developed for derivation of equations of the energy balance of disturbances for energy functionals. Based on these equations variational problems are posed for determining the critical Reynolds number of the possible beginning of the laminar-turbulent transition. Their asymptotic solutions are obtained in the limit of long-wave disturbances and yield an explicit dependence of the critical Reynolds number on the bulk viscosity coefficient, Mach number, and vibrational relaxation time. Neutral stability curves are calculated for arbitrary wavenumbers on the basis of the numerical solution of eigenvalue problems. It is shown that the minimum critical Reynolds numbers in realistic (for diatomic gases) ranges of flow parameters increase with increasing bulk viscosity coefficient, Mach number, vibrational relaxation time, and degree of excitation of vibrational modes. The results obtained in the study qualitatively confirm the asymptotic estimates for critical Reynolds number. © Springer International Publishing AG 2017.
Ключевые слова:	BULK VISCOSITY;
Издано:	2017
Физ. характеристика:	с.111-151
Цитирование:	1. Nerushev, A., Novopashin, S.: Rotational relaxation and transition to turbulence. Phys. Lett. A 232, 243–245 (1997) 2. Zhdanov, V.M., Aliyevskii, M. Ya.: Transfer and Relaxation Processes in Molecular Gases. Nauka, Moscow (1989) (in Russian) 3. Bertolotti, F.B.: The influence of rotational and vibrational energy relaxation on boundary-layer stability. J. Fluid Mech. 372, 93–118 (1998) 4. Joseph, D.D., Carmi, S.: Stability of Poiseuille flow in pipes, annuli and channels. Quart. Appl. Math. 26, 575–599 (1969) 5. Joseph, D.D.: Stability of Fluid Motion. Springer, Berlin (1976) 6. Malik, M., Dey, J., Alam, M.: Linear stability, transient energy growth, and the role of viscosity stratification in compressible plane Couette flow. Phys. Rev. E 77, 036322(15) (2008) 7. Nagnibeda, E.A., Kustova, E.V.: Non-equilibrium Reacting Gas Flows. Kinetic Theory of Transport and Relaxation Processes. Springer, Berlin (2009) 8. Mack, L.M.: Boundary-layer stability theory. Report No. 900-277, Rev. A. Jet Propulsion Laboratory, Pasadena (1969) 9. Gaponov, S.A., Maslov, A.A.: Development of Perturbations in Compressible Flows. Nauka, Novosibirsk (1980) (in Russian) 10. Grigor’ev, Yu N., Ershov, I.V.: Relaxation-induced suppression of vortex disturbances in a molecular gas. J. Appl. Mech. Tech. Phys. 44, 471–481 (2003) 11. Grigor’ev, Yu. N.: On the energetic stability theory of compressible flows. Vychisl. Tekhnol. 11, Special issue, 55–62 (2006) (in Russian) 12. Gol’dshtik, M.A., Shtern, V.N.: Hydrodynamic Stability and Turbulence. Nauka, Novosibirsk (1977) (in Russian) 13. Bronshtein, I.N., Semendyaev, K.A.: Reference Book on Mathematics. Nauka, Moscow (1986) (in Russian) 14. Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers. McGraw-Hill, New York (1961) 15. Grigor’ev, Yu. N., Ershov, I.V.: On the effect of rotational relaxation on laminar-turbulent transition. In: Abstracts Conference Dedicated to the 40-year Anniversary of the Moscow State University (Moscow, November 22–26, 1999), pp. 65–66. Izd. Mosk. Gos. Univ., Moscow (1999) (in Russian) 16. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, Berlin (1988) 17. Trefethen, L.N.: SpectralMethods in Matlab. Society for Industrial and AppliedMathematics, Philadelphia (2000) 18. Moler, C.B., Stewart, G.W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10, 241–256 (1973) 19. Grigor’ev, Yu N., Ershov, I.V.: Energy estimate of the critical Reynolds numbers in a compressible Couette flow. Effect of bulk viscosity. J. Appl.Mech. Tech. Phys. 51, 669–675 (2010) 20. Grigor’ev, Yu N., Ershov, I.V.: Effect of bulk viscosity onKelvin-Helmholtz instability. J.Appl. Mech. Tech. Phys. 49, 407–416 (2008) 21. Tamarkin, Ya. D.: Some General Problems of the Theory of Ordinary Differential Equations. Tipografiya M.P. Frolovoi, Petrograd (1917) (in Russian) 22. Naimark, M.N.: Linear Differential Operators. Nauka, Moscow (1969) (in Russian) 23. Grigor’ev, Yu N., Ershov, I.V., Ershova, E.E.: Influence of vibrational relaxation on the pulsation activity in flows of an excited diatomic gas. J. Appl. Mech. Tech. Phys. 45, 321–327 (2004)