Superfluid vortex lines in a model of turbulent flow

Physics of Fluids

Volumn 9, Issue 9, 1997, Pages 2631-2643

  Barenghi, Carlo F ^a   Samuels, David C ^a   Bauer, Gregory H ^b   Donnelly, Russell J ^c  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

^b University of Illinois at Urbana Champaign   (United States)

^c UNIVERSITY OF OREGON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CALCULATIONS; COMPUTER SIMULATION; MATHEMATICAL MODELS; REYNOLDS NUMBER; TURBULENCE; TURBULENT FLOW; VISCOSITY OF LIQUIDS; VORTEX FLOW;

SUPERFLUID VORTICITY; VORTEX LINE;

SUPERFLUID HELIUM;

FLOW PATTERNS; REYNOLDS NUMBER; TURBULENT FLOW; VORTICES;

FLOW MODELLING; REYNOLDS NUMBER; TURBULENT FLOW; VORTICES;

EID: 0031238831     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869379     Document Type: Article

References (64)

1. R. J. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991).
2. W. F. Vinen, "Mutual friction in a heat current in liquid helium II, I. Experiments on steady heat currents," Proc. R. Soc. London, Ser. A 240, 114 (1957); "Mutual friction in a heat current in liquid helium II, II. Experiments on transient effects." 240, 128 (1957). "Mutual friction in a heat current in liquid helium II, III. Theory of the mutual friction," 242, 493 (1957); "Mutual friction in a heat current in liquid helium II, IV. Critical heat currents in wide channels," 243, 400 (1957).
3. W. F. Vinen, "Mutual friction in a heat current in liquid helium II, I. Experiments on steady heat currents," Proc. R. Soc. London, Ser. A 240, 114 (1957); "Mutual friction in a heat current in liquid helium II, II. Experiments on transient effects." 240, 128 (1957). "Mutual friction in a heat current in liquid helium II, III. Theory of the mutual friction," 242, 493 (1957); "Mutual friction in a heat current in liquid helium II, IV. Critical heat currents in wide channels," 243, 400 (1957).
4. W. F. Vinen, "Mutual friction in a heat current in liquid helium II, I. Experiments on steady heat currents," Proc. R. Soc. London, Ser. A 240, 114 (1957); "Mutual friction in a heat current in liquid helium II, II. Experiments on transient effects." 240, 128 (1957). "Mutual friction in a heat current in liquid helium II, III. Theory of the mutual friction," 242, 493 (1957); "Mutual friction in a heat current in liquid helium II, IV. Critical heat currents in wide channels," 243, 400 (1957).
5. W. F. Vinen, "Mutual friction in a heat current in liquid helium II, I. Experiments on steady heat currents," Proc. R. Soc. London, Ser. A 240, 114 (1957); "Mutual friction in a heat current in liquid helium II, II. Experiments on transient effects." 240, 128 (1957). "Mutual friction in a heat current in liquid helium II, III. Theory of the mutual friction," 242, 493 (1957); "Mutual friction in a heat current in liquid helium II, IV. Critical heat currents in wide channels," 243, 400 (1957).
6. J. T. Tough. "Superfluid turbulence," in Progress in Low Temperature Physics, edited by D. F. Brewer (North-Holland, Amsterdam, 1987), Vol. VIII, p. 133: L. B. Opatowsky and J. T. Tough, "Homogeneity of turbulence in pure superflow," Phys. Rev. B 24, 5420 (1981): J. K. Kefkalidis, G. Klinich, III, and J. T. Tough, "Superfluid turbulence in a nonuniform rectangular channel," ibid. 50, 15909 (1994).
7. J. T. Tough. "Superfluid turbulence," in Progress in Low Temperature Physics, edited by D. F. Brewer (North-Holland, Amsterdam, 1987), Vol. VIII, p. 133: L. B. Opatowsky and J. T. Tough, "Homogeneity of turbulence in pure superflow," Phys. Rev. B 24, 5420 (1981): J. K. Kefkalidis, G. Klinich, III, and J. T. Tough, "Superfluid turbulence in a nonuniform rectangular channel," ibid. 50, 15909 (1994).
8. J. T. Tough. "Superfluid turbulence," in Progress in Low Temperature Physics, edited by D. F. Brewer (North-Holland, Amsterdam, 1987), Vol. VIII, p. 133: L. B. Opatowsky and J. T. Tough, "Homogeneity of turbulence in pure superflow," Phys. Rev. B 24, 5420 (1981): J. K. Kefkalidis, G. Klinich, III, and J. T. Tough, "Superfluid turbulence in a nonuniform rectangular channel," ibid. 50, 15909 (1994).
9. C. F. Barenghi, C. E. Swanson, and R. J. Donnelly, "Induced vorticity fluctuations in counterflowing He II," Phys. Rev. Lett. 48, 1187 (1982); C. E. Swanson, C. F. Barenghi, and R. J. Donnelly, "Rotation of a tangle of quantized vortex lines in He II," ibid. 50, 190 (1983): R. T. Wang, C. E. Swanson, and R. J. Donnelly, "Anisotropy and drift of a quantum vortex tangle," Phys. Rev. B 36, 5240 (1987); R. J. Donnelly, "Quantized vortices and turbulence in helium II," Annu. Rev. Fluid Mech. 25, 325 (1993).
10. C. F. Barenghi, C. E. Swanson, and R. J. Donnelly, "Induced vorticity fluctuations in counterflowing He II," Phys. Rev. Lett. 48, 1187 (1982); C. E. Swanson, C. F. Barenghi, and R. J. Donnelly, "Rotation of a tangle of quantized vortex lines in He II," ibid. 50, 190 (1983): R. T. Wang, C. E. Swanson, and R. J. Donnelly, "Anisotropy and drift of a quantum vortex tangle," Phys. Rev. B 36, 5240 (1987); R. J. Donnelly, "Quantized vortices and turbulence in helium II," Annu. Rev. Fluid Mech. 25, 325 (1993).
11. C. F. Barenghi, C. E. Swanson, and R. J. Donnelly, "Induced vorticity fluctuations in counterflowing He II," Phys. Rev. Lett. 48, 1187 (1982); C. E. Swanson, C. F. Barenghi, and R. J. Donnelly, "Rotation of a tangle of quantized vortex lines in He II," ibid. 50, 190 (1983): R. T. Wang, C. E. Swanson, and R. J. Donnelly, "Anisotropy and drift of a quantum vortex tangle," Phys. Rev. B 36, 5240 (1987); R. J. Donnelly, "Quantized vortices and turbulence in helium II," Annu. Rev. Fluid Mech. 25, 325 (1993).
12. C. F. Barenghi, C. E. Swanson, and R. J. Donnelly, "Induced vorticity fluctuations in counterflowing He II," Phys. Rev. Lett. 48, 1187 (1982); C. E. Swanson, C. F. Barenghi, and R. J. Donnelly, "Rotation of a tangle of quantized vortex lines in He II," ibid. 50, 190 (1983): R. T. Wang, C. E. Swanson, and R. J. Donnelly, "Anisotropy and drift of a quantum vortex tangle," Phys. Rev. B 36, 5240 (1987); R. J. Donnelly, "Quantized vortices and turbulence in helium II," Annu. Rev. Fluid Mech. 25, 325 (1993).
13. R. P. Slegtenhorst, G. Marees, and H. van Beelen. "Transient effects in superfluid turbulence," Physica B 113, 367 (1981); G. Marees, "Transient phenomena and nonuniform superfluid turbulence in the flow of helium II," Ph.D. thesis, Leiden University, 1986.
14. R. P. Slegtenhorst, G. Marees, and H. van Beelen. "Transient effects in superfluid turbulence," Physica B 113, 367 (1981); G. Marees, "Transient phenomena and nonuniform superfluid turbulence in the flow of helium II," Ph.D. thesis, Leiden University, 1986.
15. 4He," 38, 2398 (1988).
16. 4He," 38, 2398 (1988).
17. 4He," 38, 2398 (1988).
18. R. J. Donnelly, High Reynolds Number Flows Using Liquid and Gaseous Helium (Springer-Verlag, New York, 1991).
19. C. F. Barenghi, C. Y. Swanson, and R. J. Donnelly, "Emerging issues in helium turbulence," J. Low Temp. Phys. 100, 385 (1995).
20. 4He," proceedings of LT-21. Czech. J. Phys. 46, 35 (1996).
21. 4He," proceedings of LT-21. Czech. J. Phys. 46, 35 (1996).
22. 4He," proceedings of LT-21. Czech. J. Phys. 46, 35 (1996).
23. M. R. Smith R. J. Donnelly, N. Goldenfeld, and W. F. Vinen, "Decay of vorticity in homogeneous turbulence," Phys. Rev. Lett. 71, 2583 (1993).
24. P. L. Walstrom, J. G. Weisend, H. R. Maddocks, and S. W. VanSciver, "Turbulent flow pressure drop in various He II transfer ststem components," Cryogenics 28, 101 (1988).
25. H. Borner, T. Schmeling, and D. W. Schmidt, "Experiments of the circulation and propagation of large scale vortex rongs in He II," Phys. Fluids 26, 1410 (1983); H. Borner and D. W. Schmidt, "Investigation of large scale vortex rings in He II by acoustic measurements of circulation," in Flow of Real Fluids, Lecture Notes in Physics 235 (Springer,Berlin, 1985), p. 135.
26. H. Borner, T. Schmeling, and D. W. Schmidt, "Experiments of the circulation and propagation of large scale vortex rongs in He II," Phys. Fluids 26, 1410 (1983); H. Borner and D. W. Schmidt, "Investigation of large scale vortex rings in He II by acoustic measurements of circulation," in Flow of Real Fluids, Lecture Notes in Physics 235 (Springer,Berlin, 1985), p. 135.
27. F. Bielert and G. Stamm, "Visualization of Taylor-Couetle flow in superfluid helium," Cryogenics 33, 938 (1993); see also a discussion of this experiment in reference 8.
28. D. C. Samuels, " Velocity matching and Poiseuille pipe flow of superfluid helium," Phys. Rev. B 46, 11714 (1992).
29. R. G. K. Aarts and A. T. A. M. deWaele, "Numerical investigation of the flow properties of He II," Phys. Rev. B 50, 10069 (1994); H. Penz, R. Aarts, and A. T. A. M. deWaele, "Numerical investigations of interactions between tangles of quantized vortices and second sound," Phys. Rev. Lett. 51, 11973 (1995).
30. R. G. K. Aarts and A. T. A. M. deWaele, "Numerical investigation of the flow properties of He II," Phys. Rev. B 50, 10069 (1994); H. Penz, R. Aarts, and A. T. A. M. deWaele, "Numerical investigations of interactions between tangles of quantized vortices and second sound," Phys. Rev. Lett. 51, 11973 (1995).
31. D. C. Samuels, "Response of superfluid vortex filaments to concentrated normal fluid vorticity," Phys. Rev. B 47, 1107 (1993).
32. C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, " Friction on quantized vortices in helium II. A review," J. Low Temp. Phys. 52, 189 (1983); C, E. Swanson, W. T. Wagner, R. J. Donnelly, and C. F. Barenghi, "Calculation of frequency- and velocity-dependent mutual friction parameters in helium II," ibid. 66, 263 (1987);
33. C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, " Friction on quantized vortices in helium II. A review," J. Low Temp. Phys. 52, 189 (1983); C. E. Swanson, W. T. Wagner, R. J. Donnelly, and C. F. Barenghi, "Calculation of frequency- and velocity-dependent mutual friction parameters in helium II," ibid. 66, 263 (1987);
34. D. C. Samuels and R. J. Donnelly, "Dynamic of the interaction of rotons with quantized vortices in belium II," Phys. Rev. Lett. 65, 187 (1990); R. N. Hills and P. H. Roberts, "Superfluid mechanics for a high density of vortex lines," Arch. Rat. Mech. Anal. 66, 43 (1977).
35. D. C. Samuels and R. J. Donnelly, "Dynamic of the interaction of rotons with quantized vortices in belium II," Phys. Rev. Lett. 65, 187 (1990); R. N. Hills and P. H. Roberts, "Superfluid mechanics for a high density of vortex lines," Arch. Rat. Mech. Anal. 66, 43 (1977).
36. R. J. Arms and F. R. Hama, "Localized induction concept on a curved vortex and motion of an elliptical vortex ring," Phys. Fluids 8, 553 (1965); D. W. Moore and P. G. Saffman, "The motion of a vortex filament with axial flow," Philos. Trans. R. Soc. London, Ser. A 186, 403 (1972); P. G. Saffman," Vortex Dynamics (Cambridge University Press, Cambridge, 1992).
37. R. J. Arms and F. R. Hama, "Localized induction concept on a curved vortex and motion of an elliptical vortex ring," Phys. Fluids 8, 553 (1965); D. W. Moore and P. G. Saffman, "The motion of a vortex filament with axial flow," Philos. Trans. R. Soc. London, Ser. A 186, 403 (1972); P. G. Saffman," Vortex Dynamics (Cambridge University Press, Cambridge, 1992).
38. R. J. Arms and F. R. Hama, "Localized induction concept on a curved vortex and motion of an elliptical vortex ring," Phys. Fluids 8, 553 (1965); D. W. Moore and P. G. Saffman, "The motion of a vortex filament with axial flow," Philos. Trans. R. Soc. London, Ser. A 186, 403 (1972); P. G. Saffman," Vortex Dynamics (Cambridge University Press, Cambridge, 1992).
39. J. Koplik and H. Levine, "Vortex reconnection in superfluid helium," Phys. Rev. Lett. 71, 1375 (1993).
40. L. Greengard and V. Rokhlin, "The rapid evaluation of potential fields in 3 dimensions," Lect. Notes Math. 1360, 121 (1988).
41. S. Cprrsin, "Turbulent dissipation fluctuations," Phys. Fluids 5, 1310 (1962); H. Tennekes, "Simple model for small scale structure of turbulence," ibid. 11, 669 (1968); P. G. Saffman, in Topics of Nonlinear Physics, edited by N. Zabusky (Springer, Berlin, 1968).
42. S. Cprrsin, "Turbulent dissipation fluctuations," Phys. Fluids 5, 1310 (1962); H. Tennekes, "Simple model for small scale structure of turbulence," ibid. 11, 669 (1968); P. G. Saffman, in Topics of Nonlinear Physics, edited by N. Zabusky (Springer, Berlin, 1968).
43. S. Cprrsin, "Turbulent dissipation fluctuations," Phys. Fluids 5, 1310 (1962); H. Tennekes, "Simple model for small scale structure of turbulence," ibid. 11, 669 (1968); P. G. Saffman, in Topics of Nonlinear Physics, edited by N. Zabusky (Springer, Berlin, 1968).
44. E. D. Siggis, "Numerica; study of small scale intermittency in three dimensional turbulence," J. Fluid Mech. 107, 375 (1981); R. M. Kerr, "Higher order derivative correlations and the alignment of small scale structures in isotropic numerical turbulence," ibid. 153, 31 (1985); A. Vincent and M. Meneguzzi, "The dynamics of vorticity tubes in homogeneous turbulence," ibid. 258, 245 (1994); Z. S. She, E. Jackson, and S. A. Orszag, "Intermittent vortex structures in homogenous isotropic turbulence, " Nature (London) 344, 226 (1990).
45. E. D. Siggis, "Numerica; study of small scale intermittency in three dimensional turbulence," J. Fluid Mech. 107, 375 (1981); R. M. Kerr, "Higher order derivative correlations and the alignment of small scale structures in isotropic numerical turbulence," ibid. 153, 31 (1985); A. Vincent and M. Meneguzzi, "The dynamics of vorticity tubes in homogeneous turbulence," ibid. 258, 245 (1994); Z. S. She, E. Jackson, and S. A. Orszag, "Intermittent vortex structures in homogenous isotropic turbulence, " Nature (London) 344, 226 (1990).
46. E. D. Siggis, "Numerica; study of small scale intermittency in three dimensional turbulence," J. Fluid Mech. 107, 375 (1981); R. M. Kerr, "Higher order derivative correlations and the alignment of small scale structures in isotropic numerical turbulence," ibid. 153, 31 (1985); A. Vincent and M. Meneguzzi, "The dynamics of vorticity tubes in homogeneous turbulence," ibid. 258, 245 (1994); Z. S. She, E. Jackson, and S. A. Orszag, "Intermittent vortex structures in homogenous isotropic turbulence, " Nature (London) 344, 226 (1990).
47. E. D. Siggis, "Numerica; study of small scale intermittency in three dimensional turbulence," J. Fluid Mech. 107, 375 (1981); R. M. Kerr, "Higher order derivative correlations and the alignment of small scale structures in isotropic numerical turbulence," ibid. 153, 31 (1985); A. Vincent and M. Meneguzzi, "The dynamics of vorticity tubes in homogeneous turbulence," ibid. 258, 245 (1994); Z. S. She, E. Jackson, and S. A. Orszag, "Intermittent vortex structures in homogenous isotropic turbulence, " Nature (London) 344, 226 (1990).
48. K. W. Schwarz, "Evidence for organized small scale structure in fully developed turbulence," Phys, Rev. Lett. 64, 415 (1990); S. Douady, Y. Couder, and M. E. Brachet, "Direct observation of the intermittency of intense vorticity filaments in turbulence," ibid. 67, 983 (1991).
49. K. W. Schwarz, "Evidence for organized small scale structure in fully developed turbulence," Phys, Rev. Lett. 64, 415 (1990); S. Douady, Y. Couder, and M. E. Brachet, "Direct observation of the intermittency of intense vorticity filaments in turbulence," ibid. 67, 983 (1991).
50. F. Belin, J. Maurer, P. Tabeling, and H. Willaime, "Observations of intence filaments in fully developed turbulence," J. Phys. II 6, 573 (1996).
51. T. Dombre, U. Frisch, J. M. Greene, M. Henon, A. Mehr, and A. M. Soward, "Chaotic streamlines in the ABC flows," J. fluid Mech. 167, 353 (1986); A. D. Gilbert and S. Childress, Stretch, Twist, Fold, The Fast Dynamo (Springer, Berlin, 1995); A. D. Gilbert, N. F. Otani, and S. Childress, "Simple dynamical fast dynamos," in Solar and Planetary Dynamos, edited by M. R. E. Proctor, P. C. Matthews, and A. M. Rucklidge (Cambridge University Press, Canbridge, 1993), pp. 129-136.
52. T. Dombre, U. Frisch, J. M. Greene, M. Henon, A. Mehr, and A. M. Soward, "Chaotic streamlines in the ABC flows," J. fluid Mech. 167, 353 (1986); A. D. Gilbert and S. Childress, Stretch, Twist, Fold, The Fast Dynamo (Springer, Berlin, 1995); A. D. Gilbert, N. F. Otani, and S. Childress, "Simple dynamical fast dynamos," in Solar and Planetary Dynamos, edited by M. R. E. Proctor, P. C. Matthews, and A. M. Rucklidge (Cambridge University Press, Canbridge, 1993), pp. 129-136.
53. T. Dombre, U. Frisch, J. M. Greene, M. Henon, A. Mehr, and A. M. Soward, "Chaotic streamlines in the ABC flows," J. fluid Mech. 167, 353 (1986); A. D. Gilbert and S. Childress, Stretch, Twist, Fold, The Fast Dynamo (Springer, Berlin, 1995); A. D. Gilbert, N. F. Otani, and S. Childress, "Simple dynamical fast dynamos," in Solar and Planetary Dynamos, edited by M. R. E. Proctor, P. C. Matthews, and A. M. Rucklidge (Cambridge University Press, Canbridge, 1993), pp. 129-136.
54. D. J. Galloway and M. R. E. Proctor, "Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion," Nature (London) 356, 691 (1992); N. F. Otani, "A fast kinematic dynamo in 2-dimensional time dependent flows," J. Fluid Mech. 253, 327 (1993).
55. D. J. Galloway and M. R. E. Proctor, "Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion," Nature (London) 356, 691 (1992); N. F. Otani, "A fast kinematic dynamo in 2-dimensional time dependent flows," J. Fluid Mech. 253, 327 (1993).
56. H. K. Moffatt and A. Tsinober, "Helicity in laminar and turbulent flow," Annu. Rev. Fluid Mech. 24, 281 (1992).
57. E. Kit, A. Tsinober, and J. L. Balint, "An experimental study of helicity related properties in a turbulent flow past a grid," Phys. Fluids 30, 3328 (1987); E. Kit, A. Tsinober, M. Teitel, J. L. Balint, J. M. Wallace, and E. Levich, "Vorticity measurements in turbulent grid flows," Fluid Dyn. Res. 3, 289 (1988).
58. E. Kit, A. Tsinober, and J. L. Balint, "An experimental study of helicity related properties in a turbulent flow past a grid," Phys. Fluids 30, 3328 (1987); E. Kit, A. Tsinober, M. Teitel, J. L. Balint, J. M. Wallace, and E. Levich, "Vorticity measurements in turbulent grid flows," Fluid Dyn. Res. 3, 289 (1988).
59. C. F. Barenghi, "Vortices in the Couetie flow of helium II," Phys, Rev. B 45, 2290 (1992); K. L. Henderson, C. F. Barenghi, and C. A. Jones, "Nonlinear Taylor-Couette flow of helium II," J. Fluid Mech. 283, 329 (1995); K. L. Henderson and C. F. Barenghi, " Calculation of torque in nonlinear vortex flow of Henium II," Phys. Lett. A 191, 438 (1994).
60. C. F. Barenghi, "Vortices in the Couetie flow of helium II," Phys, Rev. B 45, 2290 (1992); K. L. Henderson, C. F. Barenghi, and C. A. Jones, "Nonlinear Taylor-Couette flow of helium II," J. Fluid Mech. 283, 329 (1995); K. L. Henderson and C. F. Barenghi, " Calculation of torque in nonlinear vortex flow of Henium II," Phys. Lett. A 191, 438 (1994).
61. C. F. Barenghi, "Vortices in the Couetie flow of helium II," Phys, Rev. B 45, 2290 (1992); K. L. Henderson, C. F. Barenghi, and C. A. Jones, "Nonlinear Taylor-Couette flow of helium II," J. Fluid Mech. 283, 329 (1995); K. L. Henderson and C. F. Barenghi, " Calculation of torque in nonlinear vortex flow of Henium II," Phys. Lett. A 191, 438 (1994).
62. D. K. Cheng, M. W. Cromar, and R. J. Donnelly, "Influence of an axial heat current on negatine ion trapping in rotating helium II," Phys, Rev. Lett. 31, 433 (1973).
63. R. M. Ostermeier and W. I. Glaberson, "Instability of vortex lines in the presence of an axial normal fluid flow," J. Low Temp. Phys. 21, 191 (1975).
64. F. Cattaneo, D. W. Hughes, and E. Kim, "Kinetic helicity, magnetic helicity and fast dynamo action," Phys. Rev. Lett. 76, 2057 (1996).