×

Numerical simulation of Rayleigh-Taylor instability in inviscid and viscous media. (English. Russian original) Zbl 1453.76005

Comput. Math. Math. Phys. 55, No. 5, 874-882 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 5, 876-885 (2015).
Summary: The Rayleigh-Taylor instability in viscous and inviscid compressible media is analyzed by applying the numerical simulation of the Euler and Navier-Stokes equations. It is shown that the development of hydrodynamic instabilities leads to the formation of an eddy cascade, which, after the onset of turbulence in the flow, corresponds to an eddy cascade developing in the energy and inertial ranges. The results reveal that the developing flows and the parameters under study are identical for both models.

MSC:

76-10 Mathematical modeling or simulation for problems pertaining to fluid mechanics
76N06 Compressible Navier-Stokes equations
76E17 Interfacial stability and instability in hydrodynamic stability
35Q31 Euler equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] L. F. Richardson, “The supply of energy from and to atmospheric eddies,” Proc. R. Soc. London A 97, 354-373 (1920). · doi:10.1098/rspa.1920.0039
[2] A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30(4), 299-303 (1941).
[3] A. M. Obukhov, “Spectral energy distribution in turbulent flow,” Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz. 5, 453-466 (1941).
[4] V. M. Ievlev, Numerical Simulation of Turbulent Flows (Nauka, Moscow, 1990) [in Russian]. · Zbl 0752.76007
[5] O. M. Belotserkovskii, A. M. Oparin, and V. M. Chechetkin, Turbulence: New Approaches (Nauka, Moscow, 2002) [in Russian].
[6] O. M. Belotserkovskii, V. A. Gushchin, and V. N. Kon’shin, “The splitting method for investigating flows of a stratified liquid with a free surface,” USSR Comput. Math. Math. Phys. 27(2), 181-191 (1987). · Zbl 0664.76140 · doi:10.1016/0041-5553(87)90175-3
[7] D. Layzer, “On the instability of superposed fluids in a gravitational field,” Astrophys. J. 122, 1-12 (1955). · doi:10.1086/146048
[8] Bell, G. I., Taylor instability on cylinders and spheres in the small amplitude approximation (1951)
[9] M. S. Plesse, “On the stability of fluid flows with spherical symmetry,” J. Appl. Phys. 25, 96-98 (1954). · Zbl 0055.18501 · doi:10.1063/1.1721529
[10] K. O. Mikaelian, “Effect of viscosity on Rayleigh-Taylor and Richtmyer-Meshkov instabilities,” Phys. Rev. 47, 375-383 (1993).
[11] N. A. Inogamov, A. Yu. Dem’yanov, and E. E. Son, Hydrodynamics of Mixing (Mosk. Fiz.-Tekh. Inst., Moscow, 1999).
[12] A. M. Oparin, “Numerical study of hydrodynamic instabilities,” Comput. Fluid Dyn. J. 10(3) (2001).
[13] L. G. Loitsyanskii, Mechanics of Liquids and Gases (Nauka, Moscow, 1978; Begell House, New York, 1996). · Zbl 0247.76001
[14] O. M. Belotserkovskii, V. A. Gushchin, and V. N. Kon’shin, “The splitting method for investigating flows of a stratified liquid with a free surface,” USSR Comput. Math. Math. Phys. 27(2), 181-191 (1987). · Zbl 0664.76140 · doi:10.1016/0041-5553(87)90175-3
[15] Belotserkovskii, O. M.; Chechetkin, V. M.; Fortova, S. V.; Oparin, A. M., The turbulence of free shear flows, 191-209 (2005)
[16] O. M. Belotserkovskii and S. V. Fortova, “Macroscopic parameters of three-dimensional flows in free shear turbulence,” Comput. Math. Math. Phys. 50(6), 1071-1084 (2010). · Zbl 1224.76064 · doi:10.1134/S0965542510060126
[17] S. V. Fortova, “Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer,” Comput. Math. Math. Phys. 53(3), 311-319 (2013). · Zbl 1274.76230 · doi:10.1134/S0965542513030056
[18] S. O. Belotserkovskii, A. P. Mirabel’, and M. A. Chusov, “Construction of a postcritical regime for plane periodic flow,” Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 14(1), 11-20 (1978).
[19] N. Inogamov, “Statistics of long-wavelength fluctuations and the expansion rate of Richtmyer-Meshkov turbulence zone,” JETP Lett. 75(11), 547-551 (2010). · doi:10.1134/1.1500718
[20] O. M. Belotserkovskii, Yu. M. Davydov, and A. Yu. Dem’yanov, “Interaction of perturbation modes under Rayleigh-Taylor instability,” Dokl. Akad. Nauk SSSR 288, 1071 (1986).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.