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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.20 No.4

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ASYMPTOTIC SOLUTIONS OF HYDRODYNAMIC INTERFACIAL INSTABILITIES IN CYLINDRICAL FLOW

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.4, pp.259-267
https://doi.org/10.7468/jksmeb.2013.20.4.259
Sohn, Sung-Ik
Sohn,, S. (2013). ASYMPTOTIC SOLUTIONS OF HYDRODYNAMIC INTERFACIAL INSTABILITIES IN CYLINDRICAL FLOW. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(4), 259-267, https://doi.org/10.7468/jksmeb.2013.20.4.259

Abstract

We present a high-order potential flow model for the motion of hydrodynamic unstable interfaces in cylindrical geometry. The asymptotic solutions of the bubbles in the gravity-induced instability and the shock-induced instability are obtained from the high-order model. We show that the model gives significant high-order corrections for the solution of the bubble.

keywords
bubble, hydrodynamic instabilities, potential-flow model, asymptotic solution

Reference

1.

(1983). Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density (170-177). Proc. London Math. Soc..

2.

(1960). Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math., 13, 297-319. 10.1002/cpa.3160130207.

3.

(1955). On the instability of superimposed fluids in a gravitational field. Astrophys. J., 122, 1-12. 10.1086/146048.

4.

(1984). An overview of Rayleigh-Taylor instability. Physica D, 12, 3-10. 10.1016/0167-2789(84)90510-4.

5.

(1989). The interaction of shock waves with fluid interfaces. Adv. Appl. Math., 10, 201-227. 10.1016/0196-8858(89)90011-0.

6.

(1999). Quantitative theory of Richtmyer-Meshkov instability in three dimensions. Zeit. Angew. Math. Phys., 50, 1-46. 10.1007/s000330050137.

7.

(2000). Robust computational algorithms for dynamic interface tracking in three dimensions. SIAM J. Sci. Comput., 21, 2040-2256.

8.

(2002). A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor Mixing. Chaos, 12, 267-274. 10.1063/1.1460942.

9.

(2012). High-resolution vortex simulations of the Richtmyer-Meshkov instability. J. Korean Phys. Soc., 60, 1037-1042. 10.3938/jkps.60.1037.

10.

(1994). Potential flow models of Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts. Phys. Fluids, 6, 4019-4030. 10.1063/1.868391.

11.

(2002). Analytic model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett., 88, 134502. 10.1103/PhysRevLett.88.134502.

12.

(2007). Bubble interaction model for hydrodynamic unstable mixing. Phys. Rev. E, 75, 066312. 10.1103/PhysRevE.75.066312.

13.

(2009). Effects of surface tension and viscosity on the growth rates of Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Phys. Rev. E, 80, 055302. 10.1103/PhysRevE.80.055302.

14.

Sohn, Sung-Ik;. (2012). A HIGH-ORDER MODEL FOR SPIKE AND BUBBLE IN IMPULSIVELY ACCELERATED INTERFACE. Korean Journal of Mathematics, 20(3), 323-331. 10.11568/kjm.2012.20.3.323.

15.

Sohn, Sung-Ik;. (2012). HIGH-ORDER POTENTIAL FLOW MODELS FOR HYDRODYNAMIC UNSTABLE INTERFACE. Journal of the Korea Society for Industrial and Applied Mathematics, 16(4), 225-234. 10.12941/jksiam.2012.16.4.225.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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