Advertisement

Coherent Structures in Fluid Dynamics

  • N. J. Zabusky
Part of the Studies in the Natural Sciences book series (SNS, volume 13)

Abstract

In the last decade we have experienced a conceptual shift in our view of turbulence. For flows with strong velocity shears, near boundaries, density gradients, magnetic fields or other organizing characteristics, many now feel that the spectral or wave-number space description has inhibited fundamental progress.

Keywords

Coherent Structure Ring Vortex Boussinesq Equation Reynolds Shear Stress Point Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abernathy, F. H. and Kronauer, R. E. The Formation of Vortex Streets, J. Fluid Mech. 13, 1, (1962).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    Achenbach, E. Experiments on Flov Past Spheres at Very High Reynolds Numbers. J. Fluid Mech. 54, 565–575, (1972).ADSCrossRefGoogle Scholar
  3. 3.
    Achenbach, E. Vortex Shedding from Spheres. J. Fluid Mech. 62, 209–221, (1974)ADSCrossRefGoogle Scholar
  4. 4.
    Ahlborn, F. Uber den Mechanismus des hydrodynamischen Widerstandes, — Hamburg, (1902).Google Scholar
  5. 5.
    Bailey, A.B. Observations of Sphere Wakes Over a Wide Range of Velocities and Ambient Pressures. Arnold Research Organization, Inc. Report AEDC-TR-68–112, (1968).Google Scholar
  6. 6.
    Basset, A.B. 1888. A Treatise or Hydrodynamics. Dover, 1961.Google Scholar
  7. 7.
    Batchelor, G.K. Homogeneous Turbulence, Cambridge University Press (1953).MATHGoogle Scholar
  8. 8.
    Bearman, P.W. On Vortex Shedding From A Circular Cylinder in the Critical Reynolds Number Regime. J. Fluid Mech. 37, 577, (1969).ADSCrossRefGoogle Scholar
  9. 9.
    Beavers, G.S. and Wilson, T.A. Vortex Growth in Jets. J. Fluid Mech. 44, 97, (1970).ADSCrossRefGoogle Scholar
  10. 10.
    Benard, H. Formation de Centres de Giration a l’arriére d’un Obstacle en Mouvement, Comp. Rend 147, 839, (1908).Google Scholar
  11. 11.
    Berger, E. and Wille, R. Periodic Flow Phenomena, Ann. Rev. Fluid Mech. 4, 313, (1972).ADSCrossRefGoogle Scholar
  12. 12.
    Berk, H.L. and Roberts, K.V. The Water-bag Model. Methods of Computational Physics, Plasma Physics, Vol. 9, 88–135, (1970).Google Scholar
  13. 13.
    Betchov, R. and Criminale, W.O. Stability of Parallel Flows, Academic Press, New York, (1967).Google Scholar
  14. 14.
    Brovand, F.K. and Weidman, P.D. Large Scales in the Developing Mixing Layer. J. Fluid Mech. 76, 127–144, (1976).ADSCrossRefGoogle Scholar
  15. 15.
    Brown, G. L. and Roshko, A. On Density Effects and Large Structure in Turbulent Mixing Layers. J. Fluid Mech. 64, 775–816, (1974)ADSCrossRefGoogle Scholar
  16. 16.
    Chorin, A. J. Numerical Study of Slightly Viscous Flow. J. Gluid Mech. 57, 785–796, (1973).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Christiansen, J. P. Numerical Simulation of Hydrodynamics “by the Method of Point Vortices. J. Comp. Physics. 13, 363–379, (1973).ADSMATHCrossRefGoogle Scholar
  18. l8.
    Christiansen, J.P. and Zabusky, N.J. Instability Coalesence and Fission of Finite-Area Vortex Structures. J. Fluid Mech. 61, 219–243, (1973).ADSMATHCrossRefGoogle Scholar
  19. 19.
    Davies, P.O.A.L. and Yule, A.J. Coherent Structures in Turbulence. J. Fluid Mech. 69, 513–537, (1975).ADSMATHCrossRefGoogle Scholar
  20. 20.
    Deem, G.S. The Origin of Cusped Waves in Layered Fluids. J. Fluid Mech., to be published. (1977).Google Scholar
  21. 21.
    Durgin, W.W. and Karlsson, S.K.F. On the Phenomenon of Vortex Street Breakdown. J. Fluid Mech. 48, 507, (1971).ADSCrossRefGoogle Scholar
  22. 22.
    Fetter, A.L. Vortices and Ions in Helium. The Physics of Liquid and Solid Helium, eds. K.H. Bennemann and J.B. Ketterson. J. Wiley and Sons. (1970).Google Scholar
  23. 23.
    Frankel, L.E. Examples of Steady Vortex Rings of Small Cross-Section in an Ideal Fluid. J. Fluid Mech. 51, 119, (1972).ADSCrossRefGoogle Scholar
  24. 24.
    Fromm, J.E. and Harlow, F.H. Numerical Solution of the Problem of Vortex Street Development, Phys. Fluids 6, 975, (1963).ADSCrossRefGoogle Scholar
  25. 25.
    Goldstine, H.H. and Von Neumann, J. “On the Principles of Large Scale Computing Machines”, in CollectedWorks of John von Neumann, ed. A. Taub, Vol. 5, pp. 1–32, Macmillan, New York, 1963. The material in this paper was first given as a talk on May 15, 1946. Also see: “Recent Theories in Turbulence”, in Collected Works of John von Neumann ed. A. Taub, Vol. 6, pp. 437–472. This paper was issued as a report in 1949.Google Scholar
  26. 26.
    Griffin, O.M. and Votaw, C.W. The Vortex Street in the Wake of a Vibrating Cylinder. J. Fluid Mech. 51, 31, (1972).ADSCrossRefGoogle Scholar
  27. 27.
    Griffin, O.M. and Ramberg, S.E. The Vortex-Street Wakes of Vibrating Cylinders. J. Fluid Mech. 66 , 553–578, (1974).Google Scholar
  28. 28.
    Hama, F.R. Three-Dimensional Vortex Pattern Behind a Circular Cylinder, J. Aerosp. Sci. 24, 156, (1957).Google Scholar
  29. 29.
    Hama, F.R. Streaklines in a Perturbed Shear Flow. Phys. Fluids 5, 644, (1962).ADSMATHCrossRefGoogle Scholar
  30. 30.
    Hama, F.R. Progressive Deformation of a Perturbed Line Vortex Filament. Phys. Fluids 6, 526, (1963).ADSMATHCrossRefGoogle Scholar
  31. 31.
    Hardin, R.H., Deem, G.S., Tappert, F.D. and Zabusky, N.J. Visualization of Properties of the Two-Dimen-sional Navier-Stokes Equation. Unpublished computer generated film produced at Bell Laboratories, Whippany, N.J. 1971.Google Scholar
  32. 32.
    Hasimoto, H. A Soliton on a Vortex Filament. J. Fluid Mech. 51, 477–485, (1972).ADSMATHCrossRefGoogle Scholar
  33. 33.
    Kochin, N.E., Compt. Rend. (Doklady) de l’Acadamie des Sciences, l’sssr 24, 18–22 (1939).Google Scholar
  34. 34.
    Kochin, N.E., Kiebel, I.A. and Roze, N.U. Theoretical Hydromechanics, Interscience, (1964).Google Scholar
  35. 35.
    Lamb, H. Hydrodynamics, Cambridge, University Press, 6th ed. (1932).MATHGoogle Scholar
  36. 36.
    Leonard, A. Proc . of the IVth Int. Conf. on Numerical Methods in Fluid Dynamics, ed. R. D. Richtmyer, P. 2U5. Springer Verlag, (1975).Google Scholar
  37. 37.
    Leonard, A. Simulation of Three-Dimensional Separated Flows with Vortex Filaments. Proc. of the Vth Int. Conf. on Numerical Fluid Dynamic s (1976). Lecture Notes in Physics, ed. R.D. Richtmyer, Springer Verlag, (1977).Google Scholar
  38. 38.
    Leslie, D.C. Developments in the Theory of Turbulence. Clarendon Press, Oxford, (1973).MATHGoogle Scholar
  39. 39.
    Magarvey, R.H. and MacLatchy, C.S. Vortices in Sphere Wakes. Cand. J. Phys. 43., 1649–1656, (1965).ADSCrossRefGoogle Scholar
  40. 40.
    Miura, A. and Sato, T. Theory of Vortex Nutation and Amplitude Oscillation in an Inviscid Shear Layer. Submitted to J. Fluid MEch. (1977).Google Scholar
  41. 41.
    Moffatt, H.K. The Degree of Knottedness of Tangled Vortex Lines. J. Fluid Mech. 35, 117–129, (1969).ADSMATHCrossRefGoogle Scholar
  42. 42.
    Montgomery, D. Individual and collaborative papers with G. Joyce, G. Knorr, Y. Salu and C.R. Seyler, Jr. in Phys. Rev. Letters, J. Plasma Phys., Phys. Fluids, 1973–1977. (1977).Google Scholar
  43. 43.
    Morikawa, G.K. and Swenson, E.V. Interacting Motion of Rectilinear Geostrophic Vortices. Phys. Fluids 14, 1058–1073, (1971).ADSCrossRefGoogle Scholar
  44. 44.
    Morkovin, M.V. Flow Around a Circular Cylinder: A Kaleidoscope of Challenging Fluid Phenomena. ASME Symposium on Fully Separated Flows , pp. 102–118. (A Fluids ENg. Div. Conference). (1964).Google Scholar
  45. 45.
    Norbury, J. A Steady Vortex Ring Close to Hills Spherical Vortex. Proc. Camb. Phil. Soc. 72, 253, (1973).MathSciNetADSCrossRefGoogle Scholar
  46. 46.
    Norbury, J. J. Fluid Mech. 57, 417–431, (1973).ADSMATHCrossRefGoogle Scholar
  47. 47.
    Onsager, L. Nuovo Cimento Suppl. 6, 279. (Supplement No. 2, Series 9). (1949).MathSciNetCrossRefGoogle Scholar
  48. 48.
    Orszag, S.A. Lecture Notes on the Statistical Theory of Turbulence. Les Houches Lectures, 1973, ed. R. Balian North-Holland, (1976).Google Scholar
  49. 49.
    Papailiou, D.D. and Lykoudis, P.S. Turbulent Vortex Streets and the Entrainment Mechanism of the Turbulent Wake. J. Fluid Mech. 62, 11–31, (1974)ADSMATHCrossRefGoogle Scholar
  50. 50.
    Patnaik, P.C., Sherman, F.S. and Corcos, G.M. A Numerical Simulation of Kelvin-Helmholtz Waves of Finite Amplitude. J. Fluid Mech. 73, 215, (1976).ADSMATHCrossRefGoogle Scholar
  51. 51.
    Pekeris, C.L. Stationary Spherical Vortices in a Perfect Fluid. Proc . Nat. Acad. Sci. 69, 2460–2462, (1972).ADSMATHCrossRefGoogle Scholar
  52. 52.
    Phillips, O.M. The Dynamics of the Upper Ocean. Cambridge University Press, (1969.Google Scholar
  53. 53.
    Prandtl, L. The Generation of Vortices...London. (1927).Google Scholar
  54. 54.
    Roberts, K.V. and Christiansen, J.P. Topics in Computational Fluid Mechanics. Compt. Phys. Comm. 3, (Suppl), 14, (1972).ADSCrossRefGoogle Scholar
  55. 55.
    Roberts, P.H. and Donnelly, R.J. Superfluid Mechanics. Ann. Rev. Fluid Mech. 6, 179–225, (1974)ADSCrossRefGoogle Scholar
  56. 56.
    Rosenhead, L. Vortex Systems in Wakes. Adv. in Appl. Mech. 3, 185 (1953).MATHCrossRefGoogle Scholar
  57. 57.
    Roshko, A. Structure of Turbulent Shear Flows. AIAA J. 14, 1349–1357, (1976).ADSCrossRefGoogle Scholar
  58. 58.
    Saffman, P.G. Lectures on Homogeneous Isotropic Turbulence, in Topics in Nonlinear Physics, ed. N.J. Zabusky, pp. 485–614, Springer-Verlag. Saffman advocates a physical-space approach to very high-Re-turbulence, pp. 567–581, (1968).CrossRefGoogle Scholar
  59. 59.
    Saffman, P.G. Structure of Turbulent Line Vortices, Phys. Fluids 16, 1181–1188, (1973).ADSMATHCrossRefGoogle Scholar
  60. 60.
    Saffman, P.G. On the Formation of Vortex Rings. Studies in Appl. Math. 54, 261–268, (1975).MathSciNetADSMATHGoogle Scholar
  61. 61.
    Sato, H. and Kuriki, K. The Mechanism of Transition in the Wake of a Thin Flat Plate Placed Parallel to a Uniform Flow. J. Fluid Mech. 11, 321, (1961).ADSMATHCrossRefGoogle Scholar
  62. 62.
    Strouhal, V. Uber eine besondere Art der Tonerregung. Ann. Phys. Chem. 5, 2l6, (1878).Google Scholar
  63. 63.
    Stuart, J. T. Nonlinear Stability Theory. Ann. Rev. Fluid Mech. 3, 347, (1971).ADSCrossRefGoogle Scholar
  64. 64.
    Taneda, S. Experimental Investigation of the Wakes Behind Cylinders and Plates at low Reynolds Numbers. J. Phys. Soc. Japan 11, 302, (1956).ADSCrossRefGoogle Scholar
  65. 65.
    Taneda, S. Oscillations of the Wake Behind a Flat Plate Parallel to the Flow. J. Phys. Soc. Japan 13, 418, (1958).ADSCrossRefGoogle Scholar
  66. 66.
    Taneda, S. Downstream Development of Wakes Behind Cylinders. J. Phys. Soc. Japan, 14, 834, (1959).ADSGoogle Scholar
  67. 67.
    Taneda, S. Experimental Investigation of Vortex Streets. J. Phys. Soc. Japan, 20, 1744 (1965).ADSCrossRefGoogle Scholar
  68. 68.
    Thorpe, S.A. Turbulence in Stably Stratified Fluids. Boundary Layer Meterology 5, 95, (1973).ADSCrossRefGoogle Scholar
  69. 69.
    Thorpe, S.A. Experiments on Instability and Turbulence in a Stratified Shear Flow. J. Fluid Mech. 61, 731, (1973).ADSCrossRefGoogle Scholar
  70. 70.
    Townsend, A.A. The Structure of Turbulent Shear Flow. Cambridge University Press, (1956).MATHGoogle Scholar
  71. 71.
    Ulam, S.M. A Collection of Mathematical Problems, Wiley, (Interscience), (1960).MATHGoogle Scholar
  72. 72.
    von Karman, Th. “Über der Mechanisms des Widerstands, den ein bewegter Körper in einer Flüssigkeit erfährt , Gottinger Nachrichten, Math. Phys. Kl. 509–519 and 547–556, (1911).Google Scholar
  73. 73.
    von Karman, Th. and Rubach, H. Über den Mechanisms des Flüssigkeits -. und Luftwiderstands Phys. Zeitschrift 13, 49–89, (1912).MATHGoogle Scholar
  74. 74.
    Widnall, S.E. The Structure and Dynamics of Vortex Filaments. Ann. Rev. Fluid Mech. 7, 141–165 (1975)ADSCrossRefGoogle Scholar
  75. 75.
    Wille, R. Karman Vortex Street, Adv. in Appl. Mech. 6, 237, (1960).Google Scholar
  76. 76.
    Winant, C.D. and Browand, F.K. Vortex Pairing: The Mechanism of Turbulent Mixing Layer Growth at Moderate Reynolds Number. J. Fluid Mech. 63, 237, (1974)ADSCrossRefGoogle Scholar
  77. 77.
    Woods, J.D. and Wiley, R.L. Billow Turbulence and Ocean Microstructure. Deep-sea Res. 19, 87, (1972).Google Scholar
  78. 78.
    Zabusky, N.J. A Synergetic Approach to Problems of Nonlinear Dispersive Wave Propagation and Interaction Nonlinear Partial Differential Equations, ed. W. Ames, p. 223, Academic Press, Inc. (1967).Google Scholar
  79. 79.
    Zabusky, N.J. and Deem, G.S. Dynamical Evolution of Two-Dimensional Unstable Shear Flows. J. Fluid Mech. 47, 353–379, (1971),ADSMATHCrossRefGoogle Scholar
  80. 80.
    Zabusky, N.J. and Roberts, K.V. Contour Dynamics for Incompressible Dissipationless Fluids, I. Algorithms, (preprint), (1972).Google Scholar
  81. 81.
    Zabusky, N.J. Solitons and Energy Transport in Nonlinear Lattices. Comp. Phys. Comm. 5, 1–10, (1973).ADSCrossRefGoogle Scholar
  82. 82.
    Zaroodny, S.J. and Greenberg, M.D. On a Vortex Street Approach to the Numerical Calculation of Water Waves. J. Comp. Phys. 11, 440–446 (1973).ADSMATHCrossRefGoogle Scholar
  83. 83.
    Zdravkovich, M.M. Smoke Observations on the Formation of Karman Vortex Street, J. Fluid Mech. 37, 491 (1969).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • N. J. Zabusky
    • 1
  1. 1.University of PittsburghPittsburghUSA

Personalised recommendations