Three-dimensional velocity field for wavy Taylor-Couette flow

Physics of Fluids

Volumn 15, Issue 4, 2003, Pages 947-960

  Akonur, Alp ^a   Lueptow, Richard M ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDERS (SHAPES); JETS; SHEAR STRESS; SURFACE PHENOMENA;

COUETTE FLOW;

FLOW OF FLUIDS;

MATHEMATICAL ANALYSIS; MODELING; PARTICLE IMAGE VELOCIMETER; REYNOLDS NUMBER; TAYLOR-COUETTE FLOW; THREE-DIMENSIONAL FLOW; VELOCITY;

EID: 0038330457     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1556615     Document Type: Article

References (47)

1. G. I. Taylor, "Stability of a viscous liquid contained between two rotating cylinder," Philos. Trans, R. Soc. London. Ser. A 223, 289 (1923).
2. E. L. Koschmieder, Benard Cells and Taylor Vortices (Cambridge University Press, Cambridge, 1993).
3. R. C. DiPrima and H. L. Swinney, "Instabilities and transition in flow between concentric rotating cylinders," in Topics in Applied Physics, Hydrodynamic Instabilities and the Transition to Turbulence, edited by H. L. Swinney and J. P. Gollub (Springer, Berlin, 1985), pp. 139-180.
4. K. Kataoka, "Taylor vortices and instabilities in circular Couette flows," in Encyclopedia of Fluid Mechanics, edited by N. P. Cheremisinoff (Gulf, Houston, 1986), Vol. 1, pp. 237-273.
5. R. J. Donnelly, "Taylor-Couette flow: The early days," Phys. Today 44 (11), 32 (1991).
6. J. P. Gollub and M. H. Freilich, "Optical heterodyne test of perturbation expansions for the Taylor instability," Phys. Fluids 19, 618 (1976).
7. T. Berland, T. Jøssang, and J. Feder, "An experimental study of the connection between the hydrodynamic and phase-transition descriptions of the Couette-Taylor instability," Phys. Scr. 34, 427 (1986).
8. R. M. Heinrichs, D. S. Cannell, G. Ahlers, and M. Jefferson, "Experimental test of the perturbation expansion for the Taylor instability at various wavenumbers," Phys. Fluids 31, 250 (1988).
9. S. T. Wereley and R. M. Lueptow, "Azimuthal velocity in supercritical circular Couette flow," Exp. Fluids 18, 1 (1994).
10. A. Davey, "The growth of Taylor vortices in flow between rotating cylinders," J. Fluid Mech. 14, 336 (1962).
11. S. T. Wereley and R. M. Lueptow, "Spatio-temporal character of supercritical circular Couette flow," J. Fluid Mech. 364, 59 (1998).
12. D. Coles, "Transition in circular Couette flow," J. Fluid Mech. 21, 385 (1965).
13. P. S. Marcus, "Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave," J. Fluid Mech. 146, 65 (1984).
14. C. A. Jones, "The transition to wavy Taylor vortices," J. Fluid Mech. 157, 135 (1985).
15. K. T. Coughlin and P. S. Marcus, "Modulated waves in Taylor-Couette flow: Part 2. Numerical simulation," J. Fluid Mech. 234, 19 (1992).
16. J. P. Gollub and H. L. Swinney, "Onset of turbulence in a rotating fluid," Phys. Rev. Lett. 35, 927 (1975).
17. A. Brandstater and H. L. Swinney, "Strange attractors in weakly turbulent Couette-Taylor flow," Phys. Rev. A 35, 2207 (1987).
18. Y. Takeda, W. E. Fischer, and J. Sakakibara, "Decomposition of the modulated waves in a rotating Couette system," Science 263, 502 (1994).
19. K. Kose, "Spatial mapping of velocity power spectra in Taylor-Couette flow using ultrafast NMR imaging," Phys. Rev. Lett. 72, 1467 (1994).
20. D. Riechelmann and K. Nanbu, "Three-dimensional simulation of wavy Taylor vortex flow by direct simulation Monte Carlo method," Phys. Fluids 9, 811 (1997).
21. C. L. Streett and M. Y. Hussaini, "A numerical simulation of the appearance of chaos in finite-length Taylor-Couette flow," Appl. Numer. Math. 7, 41 (1991).
22. S. GhoshMoulic and L. S. Yao, "Taylor-Couette instability of travelling waves with a continous spectrum," J. Fluid Mech. 324, 181 (1996).
23. K. A. Meyer, "Time-dependent numerical study of Taylor vortex flow," Phys. Fluids 10, 1874 (1967).
24. K. A. Meyer, "Three-dimensional study of flow between concentric rotating cylinders," High-Speed Computing in Fluid Dynamics: Phys. Fluids Suppl. 11 12, 11-165 (1969).
25. R. Meyer-Spasche and H. B. Keller, "Computations of the axisymmetric flow between rotating cylinders," J. Comput. Phys. 35, 100 (1980).
26. A. K. Majumdar and D. B. Spalding, "Numerical computation of Taylor vortices," J. Fluid Mech. 81, 295 (1977).
27. C. A. Jones, "Nonlinear Taylor vortices and their stability," J. Fluid Mech. 102, 249 (1981).
28. R. D. Moser, P. Moin, and A. Leonard, "A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow," J. Comput. Phys. 52, 524 (1983).
29. H. Fasel and O. Booz, "Numerical investigation of supercritical Taylor-vortex flow for a wide gap," J. Fluid Mech. 138, 21 (1984).
30. W. Schroder and H. B. Keller, "Wavy Taylor-vortex flows via multigrid-continuation methods," J. Comput. Phys. 91, 197 (1990).
31. R. P. Dring, "Sizing criteria for laser anemometry particles," ASME J. Fluids Eng. 104, 15 (1982).
32. C. E. Willert and M. Gharib, "Digital particle image velocimetry," Exp. Fluids 10, 181 (1991).
33. A. Recktenwald, M. Lücke, and H. W. Müller, "Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis," Phys. Rev. E 48, 4444 (1993).
34. C. D. Andereck, S. S. Liu, and H. L. Swinney, "Flow regimes in a circular Couette system with independently rotating cylinders," J. Fluid Mech. 164, 155 (1986).
35. W. S. Edwards, S. R. Beane, and S. Varma, "Onset of wavy vortices in the finite-length Couette-Taylor problem," Phys. Fluids A 3, 1510 (1991).
36. W. S. Edwards, R. P. Tagg, B. C. Dornblaser, and H. L. Swinney, "Periodic traveling waves with nonperiodic pressure," Eur. J. Mech. B/Fluids 10, 205 (1991).
37. G. S. Bust, B. C. Dornblaser, and E. L. Koschmieder, "Amplitudes and wavelengths of wavy Taylor vortices," Phys. Fluids 28, 1243 (1985).
38. H. A. Snyder and R. B. Lambert, "Harmonic generation in Taylor vortices between rotating cylinder," J. Fluid Mech. 26, 545 (1966).
39. D. S. Broomhead and S. C. Ryrie, "Particle paths in wavy vortices," Nonlinearity 1, 409 (1988).
40. S. C. Ryrie, "Mixing by chaotic advection in a class of spatially periodic flows," J. Fluid Mech. 236, 1 (1992).
41. P. Ashwin and G. P. King, "A study of particle paths in non-axisymmetric Taylor-Couette flows," J. Fluid Mech. 338, 341 (1997).
42. M. Rudman, "Mixing and particle dispersion in the wavy vortex regime of Taylor-Couette flow," AIChE J. 44, 1015 (1998).
43. M. Rudolph, T. Shinbrot, and R. M. Lueptow, "A model of mixing and transport in wavy Taylor-Couette flow," Physica D 121, 163 (1998).
44. G. P. King, G. Rowlands, M. Rudman, and A. N. Yannacopoulos, "Predicting chaotic dispersion with Eulerian symmetry measures: Wavy Taylor-vortex flow," Phys. Fluids 13, 2522 (2001).
45. I. Mezic, "Chaotic advection in bounded Navier-Stokes flows," J. Fluid Mech. 431, 347 (2001).
46. A. Akonur and R. M. Lueptow, "Chaotic mixing and transport in wavy Taylor Couette flow," Physica D 167, 183 (2002).
47. G. P. King, Y. Li, W. Lee, H. L. Swinney, and P. S. Marcus, "Wave speeds in wavy Taylor-vortex flow," J. Fluid Mech. 141, 365 (1984).