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Instabilities in geophysical fluid dynamics

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Hydrodynamic Instabilities and the Transition to Turbulence

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References

  1. J.G.Charney: “Planetary Fluid Dynamics”, in Dynamical Meteorology, ed. by P.Morel (Reidel, Dordrecht 1973) pp. 97–352

    Google Scholar 

  2. S.A.Thorpe: Turbulence in stably stratified fluids; a review of laboratory experiments. Boundary-Layer Meteorol. 5, 95–119 (1973)

    Google Scholar 

  3. T.Maxworthy, F.K. Browand: Experiments on rotating and stratified flows; oceanographic application, Annu. Rev. Fluid Mech. 7, 273–305 (1975)

    Google Scholar 

  4. F.S. Sherman, J.Imberger, G.M. Corcos: Turbulence and mixing in stably stratified waters. Annu. Rev. Fluid Mech. 10, 267–288 (1978)

    Google Scholar 

  5. R.Hide: “Some laboratory experiments on free thermal convection in a rotating fluid subject to a horizontal temperature gradient and their relation to the theory of the global atmospheric circulation”, in The Global Circulation of the Atmosphere, ed. by G. A. Corby (R. Meteorol. Soc., London 1969) pp. 196–221

    Google Scholar 

  6. R. Hide, P. J. Mason: Sloping convection in a rotating fluid. Adv. Phys. 24, 47–100 (1975)

    Google Scholar 

  7. P. G. Drazin: “Variations on a theme of Eady”. In Ref. 8.17, pp. 139–169

    Google Scholar 

  8. J. S. Turner: Double diffusive phenomena. Annu. Rev. Fluid Mech. 6, 37–56 (1974)

    Google Scholar 

  9. J. S. Turner: Laboratory experiments on double-diffusive instabilities. Adv. Chem. Phys. 32, 135–149 (1975)

    Google Scholar 

  10. L.Prandtl: Essentials of Fluid Dynamics (Blackie, London 1952)

    Google Scholar 

  11. D. J. Tritton: Physical Fluid Dynamics (Van Nostrand Reinhold, Wokingham 1977)

    Google Scholar 

  12. A. A. Townsend: The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge University Press, Cambridge 1976)

    Google Scholar 

  13. J.S.Turner: Buoyancy Effects in Fluids (Cambridge University Press, Cambridge 1973)

    Google Scholar 

  14. C-S. Yih: Dynamics of Nonhomogeneous Fluids (Macmillan, New York 1965)

    Google Scholar 

  15. G. K. Batchelor: An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge 1967)

    Google Scholar 

  16. H.P. Greenspan: The Theory of Rotating Fluids (Cambridge University Press, Cambridge 1968)

    Google Scholar 

  17. P. H. Roberts, A. M. Howard (eds.): Rotating Fluids in Geophysics (Academic Press, London 1978)

    Google Scholar 

  18. L. N. Howard: Fundamentals of the theory of rotating fluids. J. Appl. Mech. 30, 481–485 (1963)

    Google Scholar 

  19. M.J.Lighthill: Dynamics of rotating fluids; a survey. J. Fluid Mech. 26, 411–431 (1966)

    Google Scholar 

  20. R. Hide: Dynamics of rotating fluids. Q. J. R. Meteorol. Soc. 103, 1–28 (1977)

    Google Scholar 

  21. J. R. Holton: An Introduction to Dynamic Meteorology (Academic Press, New York 1972)

    Google Scholar 

  22. O.M.Phillips: The Dynamics of the Upper Ocean, 2nd ed. (Cambridge University Press, Cambridge 1978)

    Google Scholar 

  23. M. E. Stern: Ocean Circulation Physics (Academic Press, New York 1975)

    Google Scholar 

  24. R.Hide: Motions in planetary atmospheres. Q. J. R. Meteorol. Soc. 102, 1–23 (1976)

    Google Scholar 

  25. P.H. Stone: “The meteorology of the Jovian atmosphere”, in Jupiter, Studies of the Interior, Atmosphere, Magnetosphere, and Satellites, ed. by T.Gehrels (University of Arizona Press, Tucson 1976)

    Google Scholar 

  26. V.P.Starr: Physics of Negative Viscosity Phenomena (McGraw-Hill, New York 1968)

    Google Scholar 

  27. J. Lighthill: Waves in Fluids (Cambridge University Press, Cambridge 1978)

    Google Scholar 

  28. H. G. Moll: Die atmosphärische Umströmung Madeiras. Beitr. Phys. Atmos. 44, 227–244 (1971)

    Google Scholar 

  29. E. Berger, R. Wille: Periodic flow phenomena. Annu. Rev. Fluid Mech. 4, 313–340 (1972)

    Google Scholar 

  30. E. Palmén, C.W.Newton: Atmospheric Circulation Systems (Academic Press, New York 1969)

    Google Scholar 

  31. G. W. Platzmann: The Rossby wave. Q. J. R. Meteorol. Soc. 94, 225–248 (1968)

    Google Scholar 

  32. J. R. Bates: Dynamics of stationary ultra-long waves in middle latitudes. Q. J. R. Meteorol. Soc. 103, 397–430 (1977)

    Google Scholar 

  33. J.T.Houghton: The Physics of Atmospheres (Cambridge University Press, Cambridge 1977)

    Google Scholar 

  34. P. G. Drazin, L. N. Howard: Hydrodynamic stability of parallel flow of inviscid fluid. Adv. Appl. Mech. 9,1–89 (1966)

    Google Scholar 

  35. Y. Mori, Y. Uchida: Forced convective heat transfer between horizontal flat plates. Int. J. Heat Mass Transfer 9, 803–817 (1966)

    Google Scholar 

  36. M. Akiyama, G. J. Hwang, K. C. Cheng: Experiments on the onset of longitudinal vortices in laminar forced convection between horizontal plates. J. Heat Transfer 93, 335–341 (1971)

    Google Scholar 

  37. F. M. Richter, B.Parsons: On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80, 2529–2541 (1975)

    Google Scholar 

  38. R. M. Clever, F. H. Busse, R. E. Kelly: Instabilities of longitudinal convection rolls in Couette flow. Z. angew. Math. Phys. 28, 771–783 (1977)

    Google Scholar 

  39. D. J. Tritton: Turbulent free convection above a heated plate inclined at a small angle to the horizontal. J. Fluid Mech. 16, 282–312 (1963)

    Google Scholar 

  40. A. A. Townsend: Mixed convection over a heated horizontal plane. J. Fluid Mech. 55, 209–228 (1972)

    Google Scholar 

  41. J. W. Miles: On the stability of heterogeneous flows. J. Fluid Mech. 10, 496–508 (1961)

    Google Scholar 

  42. P.Hazel: Numerical studies of the stability of inviscid stratified shear flows. J. Fluid Mech. 51, 39–62 (1972)

    Google Scholar 

  43. K.S.Gage: Linear viscous stability theory for stably stratified shear flow; a review. Boundary-Layer Meteorol. 5, 3–17 (1973)

    Google Scholar 

  44. S. A. Maslowe: Finite-amplitude Kelvin-Helmholtz billows. Boundary-Layer Meteorol. 5, 43–52 (1973)

    Google Scholar 

  45. S. A. Maslowe: Weakly non-linear stability theory of stratified shear flows. Q. J. R. Meteorol, Soc. 103, 769–783 (1977)

    Google Scholar 

  46. P.C.Patnaik, F.S.Sherman, G.M.Corcos: A numerical simulation of Kelvin-Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215–240 (1976)

    Google Scholar 

  47. S. N. Brown, K. Stewartson: The evolution of a small inviscid disturbance to a marginally unstable stratified shear flow; stage two. Proc. R. Soc. London A 363, 175–194 (1978)

    Google Scholar 

  48. S.A.Thorpe: Experiments on the stability of stratified shear flows; miscible fluids. J. Fluid Mech. 46, 299–320 (1971)

    Google Scholar 

  49. R. S. Scotti, G. M. Corcos: An experiment on the stability of small disturbances in a stratified free shear layer. J. Fluid Mech. 52, 499–528 (1972)

    Google Scholar 

  50. F. K. Browand, C. D. Winant: Laboratory observations of shear-layer instability in a stratified fluid. Boundary-Layer Meteorol. 5, 67–77 (1973)

    Google Scholar 

  51. D.P. Delisi, G. Corcos: A study of internal waves in a wind tunnel. Boundary-Layer Meteorol. 5, 121–137 (1973)

    Google Scholar 

  52. C. G. Koop: “Instability and Turbulence in a Stratified Shear Layer”; Univ. Southern Calif., Dept. Aerospace Eng. Rep. USCAE 134 (1976)

    Google Scholar 

  53. C.G.Koop, F.K.Browand: Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135–160 (1979)

    Google Scholar 

  54. K. A. Browning: Structure of the atmosphere in the vicinity of large-amplitude Kelvin-Helmholtz billows. Q. J. R. Meteorol. Soc. 97, 283–299 (1971)

    Google Scholar 

  55. P. A. Davis, W. R. Peltier: Resonant parallel shear instability in the stratified planetary boundary layer. J. Atmos. Sci. 33, 1287–1300 (1976)

    Google Scholar 

  56. J. L. Lumley, H. A. Panofsky: The Structure of Atmospheric Turbulence (Interscience, New York 1964)

    Google Scholar 

  57. J. E. Hart: Stability of the flow in a differentially heated inclined box. J. Fluid Mech. 47, 547–576 (1971)

    Google Scholar 

  58. E. M. Sparrow, R. B. Husar: Longitudinal vortices in natural convection flow on inclined plates. J. Fluid Mech. 37, 251–256 (1969)

    Google Scholar 

  59. J. R. Lloyd, E. M. Sparrow: On the instability of natural convection flow on inclined plates. J. Fluid Mech. 42, 465–470 (1970)

    Google Scholar 

  60. D. J. Tritton: Transition to turbulence in the free convection boundary layers on an inclined heated plate. J. Fluid Mech. 16, 417–435 (1963)

    Google Scholar 

  61. W. Debler: “The Towing of Bodies in a Stratified Fluid”x; Univ. Michigan, Dept. Engng. Mech., Tech. Rep. EM-71-1 (1971)

    Google Scholar 

  62. P. W. M. Brighton: Strongly stratified flow past three-dimensional obstacles. Q. J. R. Meteorol. Soc. 104, 289–307 (1978)

    Google Scholar 

  63. A. J. Faller, R. Kaylor: Instability of the Ekman spiral with application to the planetary boundary layers. Phys. Fluids 10, Suppl. 212–219 (1967)

    Google Scholar 

  64. P. R. Tatro, E. L. Mollo-Christensen: Experiments on Ekman layer instability. J. Fluid Mech. 28, 531–543 (1967)

    Google Scholar 

  65. D. R. Caldwell, C. W. Van Atta: Characteristics of Ekman boundary layer instabilities. J. Fluid Mech. 44, 145–160 (1970)

    Google Scholar 

  66. J.P. Johnston, R. M. Halleen, D. K. Lezius: Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533–558 (1972)

    Google Scholar 

  67. D. J. Tritton: “Turbulence in rotating fluids”. In Ref. 8.17, pp. 105–138

    Google Scholar 

  68. P. Bradshaw: The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36,177–192 (1969)

    Google Scholar 

  69. J. A. Johnson: The stability of shearing motion in a rotating fluid. J. Fluid Mech. 17, 337–352 (1963)

    Google Scholar 

  70. J. E. Hart: Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341–352 (1971)

    Google Scholar 

  71. D.K.Lezius, J.P.Johnston: Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77, 153–175 (1976)

    Google Scholar 

  72. M. C. Potter, M. D. Chawla: Stability of boundary layer flow subject to rotation. Phys. Fluids 14, 2278–2281 (1971)

    Google Scholar 

  73. F. H. Busse: Shear flow instabilities in rotating systems. J. Fluid Mech. 33, 577–589 (1968)

    Google Scholar 

  74. C. E. Grosch, H. Salwen: The stability of steady and time-dependent plane Poiseuille flow. J. Fluid Mech. 34, 177–205 (1968)

    Google Scholar 

  75. P. H. Rothe, J.P. Johnston: “The Effects of System Rotation on Separation, Reattachment, and Performance in Two-Dimensional Diffusers”; Stanford Univ., Dept. Mech. Engng., Rep. PD-17 (1975)

    Google Scholar 

  76. R. Hide, C. W. Titman: Detached shear layers in a rotating fluid. J. Fluid Mech. 29, 39–60 (1967)

    Google Scholar 

  77. H. Kuo: Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere. J. Meteorol. 6, 105–122 (1949)

    Google Scholar 

  78. A.P.Ingersoll, J.N.Cuzzi: Dynamics of Jupiter's cloud bands. J. Atmos. Sci. 26, 981–985 (1969)

    Google Scholar 

  79. A.P.Ingersoll: Pioneer 10 and 11 observations and the dynamics of Jupiter's atmosphere. Icarus 29, 245–253 (1976)

    Google Scholar 

  80. E. A. Eady: Long waves and cyclone waves. Tellus 1, 33–52 (1949)

    Google Scholar 

  81. V. Barcilon: Role of the Ekman layers in the stability of the symmetric regime obtained in a rotating annulus. J. Atmos. Sci. 21, 291–299 (1964)

    Google Scholar 

  82. J. Brindley: Stability of flow in a rotating viscous incompressible fluid subject to differential heating. Phil. Trans. R. Soc. London A 253, 1–25 (1960)

    Google Scholar 

  83. J. S. A. Green: A problem in baroclinic instability. Q. J. R. Meteorol. Soc. 86, 237–251 (1960)

    Google Scholar 

  84. F. P. Bretherton: Critical layer instability in baroclinic flows. Q. J. R. Meteorol. Soc. 92, 325–334 (1966)

    Google Scholar 

  85. F.P. Bretherton: Baroclinic instability and the short wavelength cut-off in terms of potential vorticity. Q. J. R. Meteorol. Soc. 92, 335–346 (1966)

    Google Scholar 

  86. R. Hide, P. J. Mason: On the transition between axisymmetric and non-axisymmetric flow in a rotating liquid annulus subject to a horizontal temperature gradient. Geophys. Astrophys. Fluid Dyn. 10, 121–156 (1978)

    Google Scholar 

  87. P. H. Stone: On non-geostrophic baroclinic instability. J. Atmos. Sci. 23, 390–400 (1966)

    Google Scholar 

  88. P. H. Stone, S. Hess, R. Hadlock, P. Ray: Preliminary results of experiments with symmetric baroclinic instabilities. J. Atmos. Sci. 26, 997–1001 (1969)

    Google Scholar 

  89. T. Maxworthy: A review of Jovian atmospheric dynamics. Planet. Space Sci. 21, 623–641 (1973)

    Google Scholar 

  90. I. C. Walton: The viscous non-linear symmetric baroclinic instability of a zonal shear flow. J. Fluid Mech. 87, 65–84 (1975)

    Google Scholar 

  91. R. Hide: An experimental study of thermal convection in a rotating liquid. Phil. Trans. R. Soc. London A 250, 441–478 (1958)

    Google Scholar 

  92. W. W. Fowlis, R. Hide: Thermal convection in a rotating annulus of liquid: effect of viscosity on the transition between axisymmetric and non-axisymmetric flow regimes. J. Atmos. Sci. 22, 541–558 (1965)

    Google Scholar 

  93. R. L. Pfeffer, W. W. Fowlis, J. S. Fein, J. Buckley: Experimental determinations of the transitions between the symmetrical and wave regimes in a rotating differentially heated annulus of fluid. Pure Appl. Geophys. (PAGEOPH) 81, 263–271 (1970)

    Google Scholar 

  94. J. A. C. Kaiser: Rotating deep annulus convection. I. Thermal properties of the upper symmetric regime. Tellus 21, 789–804 (1969)

    Google Scholar 

  95. J. A. C. Kaiser: Rotating deep annulus convection. II. Wave instabilities, vertical stratification and associated theories. Tellus 22, 275–287 (1970)

    Google Scholar 

  96. C. B. Ketchum: An experimental study of baroclinic annulus waves at large Taylor number. J. Atmos. Sci. 29, 665–679 (1972)

    Google Scholar 

  97. J. E. Hart: A laboratory study of baroclinic instability. Geophys. Fluid Dyn. 3, 181–210 (1972)

    Google Scholar 

  98. R. Krishnamurti: “Experiments in Ocean Circulation Modelling”; Tech. Rep. 14, Dept. Oceanography, Florida State University (1977)

    Google Scholar 

  99. J. C. King: An experimental study of baroclinic wave interactions in a two-layer system. Geophys. Astrophys. Fluid Dyn. 13, 153–168 (1979)

    Google Scholar 

  100. J. S. Fein, R. L. Pfeffer: An experimental study of the effects of Prandtl number on thermal convection in a rotating differentially heated cylindrical annulus of fluid. J. Fluid Mech. 75, 81–112 (1976)

    Google Scholar 

  101. R. Hide, P. J. Mason, R. A. Plumb: Thermal convection in a rotating fluid subject to a horizontal temperature gradient: spatial and temporal characteristics of fully developed baroclinic waves. J. Atmos. Sci. 34, 930–950 (1977)

    Google Scholar 

  102. R.L.Pfeffer, Y.Chiang: Two kinds of vacillation in rotating laboratory experiments. Mon. Weather Rev. 95, 75–82 (1967)

    Google Scholar 

  103. R. L. Pfeffer, W. W. Fowlis: Wave dispersion in a rotating differentially heated cylindrical annulus of fluid. J. Atmos. Sci. 25, 361–371 (1968)

    Google Scholar 

  104. W. W. Fowlis, R. L. Pfeffer: Characteristics of amplitude vacillation in a rotating differentially heated fluid determined by a multi-probe technique. J. Atmos. Sci. 26, 100–108 (1969)

    Google Scholar 

  105. H. Stommel, A. B. Arons, D. C. Blanchard: An oceanographical curiosity: the perpetual salt fountain. Deep Sea Res. 3, 152–153 (1956)

    Google Scholar 

  106. M. E. Stern, J. S. Turner: Salt fingers and convectiog layers. Deep Sea Res. 16, 497–511 (1969)

    Google Scholar 

  107. P. F. Linden: The formation and destruction of fine structure by double-diffusive processes. Deep Sea Res. 23, 895–908 (1976)

    Google Scholar 

  108. P. F. Linden: The formation of banded salt finger structure. J. Geophys. Res. 83, 2902–2912 (1978)

    Google Scholar 

  109. R. I. Tait, M. R. Howe: Some observations of thermohaline stratification in the deep ocean. Deep Sea Res. 15, 275–280 (1968)

    Google Scholar 

  110. B. Magnell: Salt fingers observed in the Mediterranean outflow using a towed sensor. J. Phys. Oceanogr. 6, 511–523 (1976)

    Google Scholar 

  111. R. W. Schmitt, D. L. Evans: An estimate of the vertical mixing due to salt fingers based on observations in the North Atlantic Central Water. J. Geophys. Res. 83, 2913–2919 (1978)

    Google Scholar 

  112. A. E. Gargett: An investigation of the occurrence of oceanic turbulence with respect to fine structure. J. Phys. Oceanogr. 6, 139–156 (1976)

    Google Scholar 

  113. A. J. Williams: Salt fingers observed in the Mediterranean outflow. Science 185, 941–943 (1974)

    Google Scholar 

  114. H. E. Huppert, J. S. Turner: Double diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda. J. Phys. Oceanogr. 2,456–461 (1972)

    Google Scholar 

  115. M. E. Stern: The salt fountain and thermohaline convection. Tellus 12, 172–175 (1960)

    Google Scholar 

  116. G. Veronis: A finite amplitude instability in thermohaline convection. J. Mar. Res. 23, 1–17 (1965)

    Google Scholar 

  117. G. Veronis: Effect of a stabilizing gradient of solute on thermal convection. J. Fluid Mech. 34, 315–336 (1968)

    Google Scholar 

  118. P.G.Baines, A.E.Gill: On thermohaline convection with linear gradients. J. Fluid Mech. 37, 289–306 (1969)

    Google Scholar 

  119. T. G. L. Shirtcliffe: Thermosolutal convection: observation of an overstable mode. Nature 213,489–490 (1967)

    Google Scholar 

  120. S. A. Thorpe, P. K. Hutt, R. Soulsby: The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 28, 375–400 (1969)

    Google Scholar 

  121. H. E. Huppert, J. S. Turner: On melting icebergs. Nature 271, 46–48 (1978)

    Google Scholar 

  122. J. E. Hart: On sideways diffusive instability. J. Fluid Mech. 49, 279–288 (1971)

    Google Scholar 

  123. P. F. Linden, J. E. Weber: The formation of layers in a double-diffusive system with a sloping boundary. J. Fluid Mech. 81, 757–773 (1977)

    Google Scholar 

  124. P. Goldreich, G. Schubert: Differential rotation in stars. Astrophys. J. 150, 571 (1967)

    Google Scholar 

  125. C. A. Jones: The onset of shear instability in stars. Geophys. Astrophys. Fluid Dyn. 8, 165–184 (1977)

    Google Scholar 

  126. M. E. McIntyre: Diffusive destabilization of the baroclinic circular vortex. Geophys. Fluid Dyn. 1, 19–57 (1970)

    Google Scholar 

  127. D.J. Acheson: On the instability of toroidal magnetic fields and differential rotation in stars. Phil. Trans. R. Soc. London A 292, 459–500 (1978)

    Google Scholar 

  128. D. J. Baker: Density gradients in a rotating stratified fluid: experimental evidence for a new instability. Science 172, 1029–1031 (1971)

    Google Scholar 

  129. J. Calman: Experiments on high Richardson number instability of a rotating stratified shear flow. Dyn. Atmos. Ocean. 1, 277–297 (1977)

    Google Scholar 

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Harry L. Swinney PhD Jerry P. Gollub PhD

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Tritton, D.J., Davies, P.A. (1985). Instabilities in geophysical fluid dynamics. In: Swinney, H.L., Gollub, J.P. (eds) Hydrodynamic Instabilities and the Transition to Turbulence. Topics in Applied Physics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13319-4_18

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