A computational study of rising plane taylor bubbles

Journal of Computational Physics

Volumn 157, Issue 1, 2000, Pages 120-142

  Daripa, Prabir ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; TOPOLOGY;

A-PLANE; BUBBLE RISING; COMPUTATIONAL STUDIES; FAMILIES OF SOLUTIONS; NEWTON'S ITERATION; NUMERICAL COMPUTATIONS; REPRESENTATION METHOD; SERIES REPRESENTATIONS; TAYLOR BUBBLES; TRANSITION POINT;

FROUDE NUMBER;

EID: 10244278615     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6366     Document Type: Article

References (32)

1. G. Baker, R. Caflisch, and M. Siegel, Singularity formation during Rayleigh-Taylor instability, J. Fluid Mech. 252, 51 (1993).
2. G. Birkhoff, Taylor Instability and Laminar Mixing, Los Alamos Report LA-1862 (1954), p. 1.
3. G. Birkhoff, Taylor Instability, Appendices to Report LA-1862, Los Alamos Report LA-1927 (1956), p. 1.
4. G. Birkhoff and D. Carter, Rising plane bubbles, J. Math. Phys. 6, 769 (1957).
5. R. Combescot, T. Dombre, V. Hakim, Y. Pomeau, and A. Pumir, Shape selection for Saffman-Taylor fingers, Phys. Rev. Lett. 56, 2036 (1986).
6. R. Combescot, T. Dombre, V. Hakim, Y. Pomeau, and A. Pumir, Analytic theory of the Saffman-Taylor fingers, Phys. Rev. A 37, 1270 (1988).
7. B. Coüet, G. Strumolo, and A. E. Dukler, Modelling two-dimensional large bubbles in a rectangular channel of finite width, Phys. Fluids 29, 2367 (1986).
8. B. Couët and G. S. Strumolo, The effects of surface tension and tube inclination on a two-dimensional rising bubble, J. Fluid Mech. 184, 1 (1987).
9. P. Daripa, A numerical investigation of some pattern selection issues in the rising plane Taylor-bubble problem, J. Comput. Phys. 121(1), 129 (1995).
10. P. Daripa, Pointed Taylor bubble revisited, J. Comput. Phys. 123(1), 226 (1996).
11. R. M. Davies and G. I. Taylor, The mechanics of large bubbles rising through extended liquids and through liquids in tubes, Proc. R. Soc. London Ser. A 200, 375 (1950).
12. C. Domb and M. F. Sykes, On the susceptability of a ferromagnetic above the Curie point, Proc. R. Soc. London Ser. A 240, 214 (1957).
13. P. R. Garabedian, On steady-state bubbles generated by Taylor instability, Proc. R. Soc. London Ser. A 241, 423 (1957).
14. P. R. Garabedian, A remark about pointed bubbles, Comm. Pure Appl. Math. 38, 609 (1985).
15. P. R. Garabedian, Private Communication, November 1996.
16. S. D. Howison, J. R. Ockendon, and A. A. Lacey, Singularity development in moving-boundary problems, Quart. J. Mech. Appl. Math. 38(3), 343 (1985).
17. S. D. Howison, Fingering in Hele-Shaw cells, J. Fluid Mech. 167, 439 (1986).
18. S. D. Howison, A. A. Lacey, and J. R. Ockendon, Nonuniqueness in singular viscous fingering, Hele-Shaw free-boundary problems with suction, Quart. J. Mech. Appl. Math. II 41, 183 (1988).
19. D. A. Kessler and H. Levine, Velocity selection for Taylor bubbles, Phys. Rev. A 39, 5462 (1989).
20. M. D. Kruskal and H. Segur, Asymptotics beyond all orders in a model of crystal growth, Stud. Appl. Math. 85, 129 (1991).
21. M. S. Longuet-iggins, On the forming of sharp corners at a free surface, Proc. R. Soc. London Ser. A 371, 453 (1980).
22. D. W. Moore, The spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proc. R. Soc. London Ser. A 365, 105 (1979).
23. D. W. Moore, Numerical and analytical aspects of Helmholtz instability, in Theoretical and Applied Mechanics, edited by F. I. Niordoson and N. Olhoff (Elsevier, Amsterdam/New York, 1985).
24. M. A. Peterson, Nonuniqueness in singular viscous fingering, Phys. Rev. Lett. 62, 284 (1989).
25. S. Tanveer, Viscous displacements in a Hele-Shaw cell, in Asymptotics Beyond All Orders, edited by H. Segur, S. Tanveer, and H. Levine, NATO ASI Series B, Physics (Plenum, New York, 1991), Vol. 284.
26. S. Tanveer, Analytic theory for the selection of Saffman-Taylor finger, Phys. Fluids 30, 1589 (1987).
27. G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, I, Proc. R. Soc. London Ser. A 201, 192 (1950).
28. J.-M. Vanden-Broeck, Bubbles rising in a tube and jets falling from a nozzle, Phys. Fluids 27, 1090 (1984).
29. J.-M. Vanden-Broeck, Rising bubbles in a two dimensional tube with surface tension, Phys. Fluids 27, 2604 (1984).
30. J.-M. Vanden-Broeck, Pointed bubbles rising in a two dimensional tube, Phys. Fluids 29, 1343 (1986).
31. M. Van-Dyke, Computer-extended series, Ann. Rev. Fluid Mech. 16, 287 (1984).
32. A. Zygmund, Trigonometric Series (Cambridge Univ. Press, Cambridge, UK, 1968), Vol. 1.