Helicity in laminar and turbulent flow

Annual Review of Fluid Mechanics

Volumn 24, Issue 1, 1992, Pages 281-312

  Moffatt, H K ^a   Tsinober, A ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Euler equations; Relaxation; Topological constraints; Turbulence

Indexed keywords

HELICITY; MODELLING-MATHEMATICAL;

EID: 0026804003     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fl.24.010192.001433     Document Type: Article

References (128)

1. Achenbach, E. 1974. Vortex shedding from spheres. J. Fluid Mech. 62: 209-21
2. André, J. C., Lesieur, M. 1977. Influence of helicity on the evolution of isotropic turbulence at high Reynolds number. J. Fluid Mech. 81: 187-207
3. Aref, H., Zawadski 1991. Preprint
4. Arnold, V. I. 1974. The asymptotic Hopf invariant and its applications. Proc. Summer School in Differential Equations, Erevan, Armenian SSR Acad. Sci. Transl. 1986, in Sel. Math. Sov. 5: 327-45 (From Russian)
5. Arnold, V. I. 1974. The asymptotic Hopf invariant and its applications. Proc. Summer School in Differential Equations, Erevan, Armenian SSR Acad. Sci. Transl. 1986, in Sel. Math. Sov. 5: 327-45 (From Russian)
6. Arnold, V. I., Khesin, B. A. 1992. Topological methods in Hydrodynamics. Annu. Rev. Fluid Mech. 24: 145-66
7. Ashurst, W. T., Kerstein, A. R., Kerr, R. M., Gibson, P. H. 1987. Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30: 2343-53
8. Bajer, K., Moffatt, H. K. 1990. On a class of steady confined Stokes flows with chaotic streamlines. J. Fluid Mech. 212: 337-63
9. Bandyopadhyay, P. R. 1986. Aspects of equilibrium puffin transitional pipe flow. J. Fluid Mech. 163: 439-58
10. Batchelor, G. K., Gill, A. E. 1962. Analysis of stability of axisymmetric jets. J. Fluid Mech. 14: 529-51
11. Benjamin, T. B. 1976. The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics. In Lecture Notes in Mathematics, no. 503, ed. P. Germain, B. Nayroles, pp. 8-29. Berlin: Springer-Verlag
12. Berger, M. A., Field, G. B. 1984. The topological properties of magnetic helicity. J. Fluid Mech. 147: 133-48
13. Bojarevičs, V., Shcherbinin, E. V. 1983. Azimuthal rotation in the axisymmetric meridional flow due to an electric-current source. J. Fluid Mech. 126: 413-50
14. Brachet, M. E., Meiron, D. I., Orszag, S. A., Nichel, B. G., Morf, R. H., Frisch, U. 1983. Small-scale structure of the Taylor-Green vortex. J. Fluid Mech. 130: 411-52
15. Braginskii, S. I. 1964a. Self excitation of a magnetic field during the motion of a highly conducting fluid. Sov. Phys.-JETP 20: 726-35
16. Browand, F. K., Laufer, J. 1977. The role of large scale structures in the initial development of circular jets. In Fourth Symposium on Turbulence in Liquids, ed. J. L. Zakin, G. K. Patterson, pp. 333-44. Princeton: Science
17. Chan, Y. Y. 1977. Wavy like eddies in a turbulent jet. AIAA J. 15: 992-1001
18. Crow, S. C., Champagne, F. M. 1971. Orderly structure in jet turbulence. J. Fluid Mech. 48: 547-91
19. Dimotakis, P. E., Miyake-Lye, R. C., Papantoniu, D. A. 1983. Structure and dynamics of round turbulent jets. Phys. Fluids 26: 3185-92. For more details see Papantoniu, D. A. 1985. Observations in turbulent buoyant jets by use of laser-induced fluorescence. PhD thesis. Cal. Tech.
20. Dimotakis, P. E., Miyake-Lye, R. C., Papantoniu, D. A. 1983. Structure and dynamics of round turbulent jets. Phys. Fluids 26: 3185-92. For more details see Papantoniu, D. A. 1985. Observations in turbulent buoyant jets by use of laser-induced fluorescence. PhD thesis. Cal. Tech.
21. Dombre, T., Frisch, U., Greene, J. M., Hénon, M., Mehr, A., Soward, A. M. 1986. Chaotic streamlines in the ABC flows. J. Fluid Mech. 167: 353-91
22. Dracos, T., Kholmyansky, M., Kit, E., Tsinober, A. 1990. Some experimental results on velocity-vorticity gradients measurements in turbulent grid flows. See Moffatt & Tsinober, 1990, pp. 564-84
23. Escudier, M. 1984. Observations of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids 2: 189-96
24. Escudier, M. 1988. Vortex breakdown: observations and explanations. Progr. Aerosp. Sci. 25: 189-229
25. Etling, D. 1985. Some aspects of helicity in atmosphere flows. Beitr. Phys. Atmos. 58: 88-100
26. Foss, J. F., Wallace, J. M. 1989. The measurements of vorticity in transitional and fully developed turbulent flows. In Advances in Fluid Mechanics Measurements, ed. M. Gad El-Hak, Lect. Notes Eng. 45: 263-321. Springer-Verlag
27. Freedman, M. H. 1988. A note on topology and magnetic energy in incompressible perfectly conducting fluids. J. Fluid Mech. 194: 549-51
28. Frisch, U., She, Z. S., Sulem, P. L. 1987. Large-scale flow driven by the anisotropic kinetic alpha effect. Physica 28D: 382-92
29. Gilbert, A. D. 1988. Spiral structures and spectra in two-dimensional turbulence. J. Fluid Mech. 193: 475-97
30. Goldshtik, M. A., Zhdanova, E. M., Shtern, V. N. 1983. Spontaneous twisting of a submerged jet. Sov. Phys.-Dokl. 29: 615-17
31. Goldshtik, M. A., Zhdanova, E. M., Shtern, V. N. 1985. Occurrence of rotational motion resulting from hydrodynamic instability. Fluid Dyn. 20: 707-14
32. Grossman, L. M., Li, H., Einstein, H. 1958. Turbulence in civil engineering. Investigation of liquid shear flow by electromagnetic induction. Proc. Am. Soc. Civ. Eng. J. Hydraul. Div. 83: 1-15
33. Hauf, T. 1985. Rotating clouds within cloud streets. Beitr. Phys. Atmos. 58: 380-98
34. Herring, J. R., Metais, O. 1989. Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202: 97-115
35. Hicks, W. M. 1899. Researches in vortex motion - Part III On spiral or gyrostatic vortex aggregates. Philos. Trans. R. Soc. London Ser. A 192: 33-101
36. Hussain, F. 1986. Coherent structures and turbulence. J. Fluid Mech. 173: 303-56
37. Hussain, F., Moser, R., Colomius, T., Moin, P., Rogers, M. M. 1988. Dynamics of coherent structures in a plane mixing layer. In Studying Turbulence Using Numerical Simulation Databases - II, Report CTR-S88, pp. 49-55. NASA Ames Res. Ctr. - Stanford Univ.
38. Kambe, T. 1969. The stability of an axisymmetric jet with a parabolic profile. J. Phys. Soc. Jpn. 26: 566-75
39. Kawakubo, T., Tsuchia, Y., Sugaya, M., Matsumura, K. 1978. Formation of vortex around a sink: a kind of phase transition in nonequilibrium open system. Phys. Lett. 68A: 65-66
40. Kelvin, Lord 1869. On vortex motion. Trans. Roy. Soc. Edin. 25: 217-60
41. Kerr, R. M. 1985. Higher-order derivative correlations and the alignment of smallscale structures in isotropic numerical turbulence. J. Fluid Mech. 153: 31-58
42. Kerr, R. M. 1987. Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett. 59: 786
43. Kholmyansky, M., Kit, E., Teitel, M., Tsinober, A. 1991. Some experimental results on velocity-vorticity measurements in turbulent grid flows with controlled sign of mean helicity. Fluid Dyn. Res. 7: 65-75
44. Kida, S., Takaoka, M. 1988. Reconnection of vortex tubes. Fluid Dyn. Res. 3: 257-61
45. Kit, E., Levich, E., Shtilman, L., Tsinober, A. 1988. Coherence and symmetry breaking in turbulence: theory and experiment. Phys. Chem. Hydro. 10: 615-23
46. Kit, E., Tsinober, A., Balint, J. L., Wallace, J. M., Levich, E. 1987. An experimental study of helicity related properties of a turbulent flow past a grid. Phys. Fluids 30: 3323-25
47. Kit, E., Tsinober, A., Teitel, M., Balint, J. L., Wallace, J. M., Levich, E. 1988. Vorticity measurements in turbulent grid flows. Fluid Dyn. Res. 3: 289-94
48. Kraichnan, R. H., Panda, R. 1988. Depression of nonlinearity in decaying isotropic turbulence. Phys. Fluids 31: 2395-97
49. Krasny, R. 1986. Desingularisation of periodic vortex sheet roll-up. J. Comput. Phys. 65: 292-313
50. Krause, F., Rudiger, G. 1974. On the Reynolds stresses in mean-field hydrodynamics. Astron. Nachr. 295: 93-99
51. Krause, F., Rädler, K.-H. 1980. Mean-field Magnetohydrodynamics and Dynamo Theory. Oxford: Pergamon
52. Leibovich, S. 1991. Vortex breakdown: a coherent transition trigger in concentrated vortices. In Turbulence and Coherent Structures, ed. M. Lesieur, O. Metais, pp. 285-302. Dordrecht: Kluwer
53. Lessen, M., Singh, P. J. 1973. The stability of axisymmetric free shear layers. J. Fluid Mech. 60: 343-457
54. Levi, Y. 1988. MS thesis, Technion, Haifa
55. Levich, E., Shtilman, L. 1988. Coherence and large fluctuations of helicity in homogeneous turbulence. Phys. Lett. A126: 243-48
56. Levich, E., Tsinober, A. 1983. Helical structures, fractal dimensions and renor malisation group approaches in homogeneous turbulence. Phys. Lett. 96A: 292-98
57. Levy, Y., Seginer, A., Degani, P. 1990. Graphical visualization of vortical flows by means of helicity. AIAA J. 28: 1347-52
58. Lilly, D. K. 1982. The development and maintenance of rotation in convective storms. In Intense Atmospheric Vortices, ed. L. Bengtsson, J. Lighthill. pp. 149-60. Berlin: Springer-Verlag
59. Lilly, D. K. 1986. The structure, energetics and propagation of rotating convective storms. Part II: Helicity and storm stabilization. J. Atmos. Sci. 43: 126-40
60. Lopez, J. L., Kurzweg, V. H. 1977. Amplification of helical disturbances in a round jet. Phys. Fluids 20: 860-61
61. Malkus, W. V. R., Proctor, M. R. E. 1975. The macrodynamics of α-effect dynamos in rotating fluids. J. Fluid Mech. 67: 417-44
62. Melander, M. V., Hussain, F. 1988. Cut and connect of two antiparallel vortex tubes. In Studying Turbulence Using Numerical Simulation Databases - II, Report CTR-S88, pp. 257-86
63. Melander, M. V., Hussain, F. 1990. Topological aspects of vortex reconnection. In Topological Fluid Mechanics, ed. H. K. Moffatt, A. Tsinober, pp. 484-99. Cambridge: Cambridge Univ. Press
64. Moffatt, H. K. 1969. The degree of knottedness of tangled vortex lines. J. Fluid Mech. 36: 117-29
65. Moffatt, H. K. 1970. Dynamo action associated with random inertial waves in a rotating conducting fluid. J. Fluid Mech. 44: 705-19
66. Moffatt, H. K. 1972. An approach to a dynamic theory of dynamo action in a rotating conducting fluid. J. Fluid Mech. 53: 385-99
67. Moffatt, H. K. 1978. Magnetic Field Generation in Electrically Conducting Fluids. Cambridge: Cambridge Univ. Press
68. Moffatt, H. K. 1983. Transport effects associated with turbulence, with particular attention to the influence of helicity. Rep. Prog. Phys. 46: 621-64
69. Moffatt, H. K. 1984. Simple topological aspects of turbulent vorticity dynamics. In Turbulence and Chaotic Phenomena in Fluids, ed. T. Tatsumi, pp. 223-30. Elsevier
70. Moffatt, H. K. 1985. Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology Part I, Fundamentals. J. Fluid Mech. 159: 359-78
71. Moffatt, H. K. 1986a. Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology Part II, Stability considerations. J. Fluid Mech. 166: 359-78
72. Moffatt, H. K. 1986b. On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid. J. Fluid Mech. 173: 289-302
73. Moffatt, H. K. 1988. Generalised vortex rings with and without swirl. Fluid Dyn. Res. 3: 22-30
74. Moffatt, H. K. 1990a. Fixed points of turbulent dynamical systems and suppression of nonlinearity. In Whither Turbulence?, ed. J. L. Lumley, pp. 250-57. New York: Springer-Verlag
75. Moffatt, H. K. 1990b. The energy spectrum of knots and links. Nature 347: 367-69
76. Moffatt, H. K. 1991. Spiral structures in turbulent flow. Proc. IMA Conf. "Wavelets, Fractals and Fourier Transforms". Cambridge, Dec. 1990
77. Moffatt, H. K., Proctor, M. R. E. 1982. The role of the helicity spectrum function in turbulent dynamo theory. Geophys. Astrophys. Fluid Dyn. 21: 265-83
78. Moffatt, H. K., Tsinober, A., eds. 1990. Topological Fluid Mechanics. Cambridge: Cambridge Univ. Press
79. Moiseev, S. S., Sagdeev, R. Z., Tur, A. V., Khomenko, G. A., Yanovskii, V. V. 1983. Sov. Phys. J. Exp. Theor. Phys. 58: 1149
80. Monkewitz, P. A. 1988. A note on vortex shedding from axisymmetric bluff bodies. J. Fluid Mech. 192: 561-75
81. Moreau, J.-J. 1961. Constants d'un ilot tourbillonnaire en fluide parfait barotrope. C. R. Acad. Sci. Paris 252: 2810-12
82. Morris, P. J. 1976. The spatial viscous instability of axisymmetric jets. J. Fluid Mech. 77: 511-29
83. Onsager, L. 1931a. Reciprocal relations in irreversible processes I. Phys. Rev. 37: 405
84. Onsager, L. 1931b. Reciprocal relations in irreversible processes II. Phys. Rev. 38: 2265
85. Orszag, S. A., Pelz, R. B., Bayly, B. B. 1986. Secondary instabilities, coherent structures and turbulence. In Supercomputers and Fluid Dynamics, ed. K., Kuwahera, R. Mendez, S. A. Orszag, Lect. Notes Eng. 27: 1-14
86. Parker, E. N. 1955. Hydromagnetic dynamo models. Astrophys. J. 122: 293-314
87. Parker, E. N. 1979. Cosmical Magnetic Fields. Oxford: Clarendon
88. Pelz, R. B., Shtilman, I., Tsinober, A. 1986. On the helical nature of enforced turbulent flows. Phys. Fluids 29: 3506-8
89. Pelz, R. B., Yakhot, V., Orszag, S. A., Shtilman, L., Levich, E. 1985. Velocity-vorticity patterns in turbulent flow. Phys. Rev. Lett. 54: 2505-8
90. Plaschko, P. 1979. Helical instabilities of slowly divergent jets. J. Fluid Mech. 92: 209-15
91. Polifke, W., Levich, E. 1990. Entangledness of vortex lines in turbulent flows. See Moffatt & Tsinober, 1990, pp. 637-56
92. Polifke, W., Shtilman, L. 1989. The dynamics of decaying helical turbulence. Phys. Fluids A1: 2025-33
93. Polifke, W. 1991. Statistics of helicity fluctuations in homogeneous turbulence. Phys. Fluids A3: 115-29
94. Roberts, P. H., Stix, M. 1971. The turbulent dynamo: a translation of a series of papers by F. Krause, K.-H. Rädler and M. Steenbeck. Tech. Note 69, NCAR, Boulder, Colo.
95. Rogers, M. M., Moin, P. 1987. Helicity fluctuations in incompressible turbulent flows. Phys. Fluids 30: 2662-71
96. Sabot, J., Comte-Bellot, G. 1976. Intermittency of coherent structures in the core region of fully developed turbulent pipe flow. J. Fluid Mech. 74: 767-96
97. Scholz, D. 1986. Kohärente Wirbelstructuren im Nachlauf einer ruhenden und einer schwingungserregten Kreisscheibe. DFVLR-Forschungsbericht 86-04, 174 pp.
98. She, Z. S., Orszag, S. A., Jackson, E. 1990. Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344: 226-28
99. Shepherd, T. G. 1990. A general method for finding extremal energy states of Hamiltonian dynamical systems with applications to perfect fluids. J. Fluid Mech. 213: 573-87
100. Shingubara, S., Hagiwara, K., Fukushima, R., Kawakubo, T. 1988. Vortices around a sink hole: phase diagram for one-celled and two-celled vortices. J. Phys. Soc. Jpn. 57: 88-94
101. Shtilman, L., Levich, E., Orszag, S. A., Pelz, R. B., Tsinober, A. 1985. On the role of helicity in complex fluid flows. Phys. Lett. 113: 32-37
102. Shtilman, L., Pelz, R., Tsinober, A. 1988. Numerical investigation of helicity in turbulent flow. Comput. Fluids 16: 341-47
103. Shtilman, L., Polifke, W. 1989. On the mechanism of the reduction of nonlinearity in the incompressible Navier-Stokes equation. Phys. Fluids A1: 778-80
104. Soward, A. M. 1975. Random waves and dynamo action. J. Fluid Mech. 69: 145-77
105. Stahl, B. 1986. Experimenteller Beitrag zur Schallerzuegung durch die Turbulenz in einer Rohrstromung hinter einer unstetigen Querschnittserweiterung. Dissertation, DFVLR-FB 86-06
106. Steenbeck, M., Krause, F., Rädler, K.-H. 1966. A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion, under the influence of Coriolis forces. Z. Naturforsch. 21a: 369-76. Transl. in Roberts & Stix 1971, pp. 29-47 (From German)
107. Strange, P. J. R., Crighton, D. G. 1983. Spinning modes on axisymmetric jets. J. Fluid Mech. 134: 231-45
108. Sulem, P. L., She, Z. S., Schroll, H., Frisch, U. 1989. Generation of large-scale structures in three-dimensional flow lacking parity invariance. J. Fluid Mech. 205: 341-58
109. Synge, J. L., Lin, C. C. 1943. On a statistical model of isotropic turbulence. Trans. R. Soc. Can. Sec. III: 45-79
110. Taylor, G. I. 1921. Diffusion by continuous movements. Proc. Lond. Math. Soc. A 20: 196-211
111. Taylor, J. B. 1974. Relaxation of toroidal plasma and generation of reversed magnetic fields. Phys. Rev. Lett. 33: 1139
112. Taylor, J. B. 1986. Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 58: 741-63
113. Torrance, K. E. 1979. Natural convection in thermally stratified enclosures with localized heating from below. J. Fluid Mech. 95: 477-95
114. Tseskis, A. L., Tsinober, A. 1974. Some processes involving anomalous energy transfer over the turbulence spectrum. Magnetohydrodynamics 10: 261-63
115. Tsinober, A., Levich, E. 1983. On the helical nature of three dimensional coherent structures in turbulent flows. Phys. Lett. 99A: 321-23
116. Tsinober, A., Kit, E., Teitel, M. 1987. On the relevance of potential difference methods for turbulence measurements. J. Fluid Mech. 175: 447-61
117. Tsinober, A., Kit, E., Teitel, M. 1988. Spontaneous symmetry breaking in turbulent grid flow. Presented at the 17th IUTAM Congress, Grenoble, August 21-27, 1988
118. Tsinober, A. 1990. Turbulent drag reduction versus structure of turbulence. In Structure of Turbulence and Drag Reduction, ed. A. Gyr, pp. 313-40. Berlin: Springer-Verlag
119. Tsinober, A., Kit, E., Dracos, T. 1991. Measuring invariant (frame independent) quantities composed of velocity derivatives in turbulent flows. In Advances in Turbulence 3, ed. A. V. Johansson, P. H. Alfredsson, pp. 514-23. Berlin, Heidelberg: Springer-Verlag
120. Tsinober, A., Kit, E., Dracos, T. 1990. Experimental investigation of the field of velocity gradients in turbulent flows. Submitted to J. Fluid Mech.
121. Vallis, G. K., Carnevale, G. F., Young, W. R. 1989. Extremal energy properties and construction of stable solutions of the Euler equations. J. Fluid Mech. 207: 133-52
122. Wallace, J. M., Balint, J. L. 1990. An experimental study of helicity and related properties in turbulent flows. See Moffatt & Tsinober, 1990, pp. 585-97
123. Whitehead, J. H. C. 1947. An expression of Hopf's invariant as an integral. Proc. Natl. Acad. Sci. USA 33: 117
124. Woltjer, L. 1958. A theorem on force-free magnetic fields. Proc. Natl. Acad. Sci. USA 44: 489-91
125. Yamamoto, K., Hosokawa, I. 1981. A numerical study of inviscid helical turbulence. J. Phys. Soc. Jpn. 50: 343-48
126. Zeldovich, Y. B., Ruzmaikin, A. A., Sokoloff, D. D. 1983. Magnetic Fields in Astrophysics. London: Gordon & Breach
127. Balint, J.-L., Vukoslavčevič, P., Wallace, J. M. 1987. A study of the vertical structure of the turbulent boundary layer. In Advances in Turbulence, ed. G. Comte-Bellot, J. Mathieu, pp. 456-64. Berlin: Springer-Verlag
128. Helmholtz, H. 1858. On integrals of the hydrodynamic equations which express vortex-motion. Transl. P. G. Tait, 1867, in Phil. Mag. (4) 33: 485-512