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Eddy Dynamics and Kinematics of Convective Turbulence

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Buoyant Convection in Geophysical Flows

Part of the book series: NATO ASI Series ((ASIC,volume 513))

Abstract

This review of ‘convective’ turbulence focusses on mechanisms that determine how eddies are formed, grow and interact with each other. It is shown how these are related to the interactions of the turbulence with the rigid surfaces and other regions of fluid motion bounding the convective layer. The effects of weak cross winds and non-uniformity in surface conditions are also discussed.

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References

  1. Adrian, R.J., Ferreira, R.T.D.S. and Boberg, T. (1986) Turbulent thermal convection in wide horizontal fluid layers, Experiments in Fluids 4, 121–141.

    Google Scholar 

  2. Batchelor, G. K. (1954) Heat convection and buoyancy effects in fluids, Q. J. Roy. Met. Soc. 80, 339–358.

    Article  Google Scholar 

  3. Batchelor, G. K. (1967) Introduction to Fluid Dynamics, Cambridge University Press, Cambridge.

    Google Scholar 

  4. Batchelor, G.K. (1987) Stability of a large gas bubble rising through liquid, J. Fluid Mech. 184, 399–422.

    Article  Google Scholar 

  5. Batchelor, G.K., Canuto, V.M. and Chasnov, J.R. (1991) Homogeneous buoyancygenerated turbulence, J. Fluid Mech. 235, 349–378.

    Article  Google Scholar 

  6. Belcher, S.E. and Hunt, J.C.R. (1993) Turbulent shear flow over slowly moving waves, J. Fluid Mech. 251, 109–148.

    Article  Google Scholar 

  7. Bhat, G.S. and Narasimha, R. (1996) A volumetrically heated jet: large-eddy structure and entrainment characteristics, J. Fluid Mech. 325, 303–330.

    Article  Google Scholar 

  8. Bonnet, J.P. and Glauser, M.N. (eds.) (1993) Eddy structure identification in free turbulent shear flows, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  9. Brost, R.A. and Wyngaard, J.C. (1978) A model study of the stably stratified planetary boundary layer, J. Atmos. Sci. 25, 1427–1440.

    Article  Google Scholar 

  10. Carruthers, D.J. and Moeng, C.-H. (1987) Waves in the overlying inversion of the convective boundary layer, J. Atmos. Sci. 44, 1801–1808.

    Article  Google Scholar 

  11. Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X., Zaleski, S. and Zanetti, G. (1989) Scaling of hard thermal turbulence in Rayleigh-Bénard convection, J. Fluid Mech. 204, 1–30.

    Article  Google Scholar 

  12. Chandrasekhar, S. (1961) Hydrodynamic and hydromagnetic stability, Clarendon, Oxford.

    Google Scholar 

  13. Chapman, C.J. and Proctor, M.R.E. (1980) Nonlinear Rayleigh-Bénard convection between poorly conducting boundaries, J. Fluid Mech. 101, 759–782.

    Article  Google Scholar 

  14. Chatwin, P.C. and Sullivan, P.J. (1979) The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow J. Fluid Mech. 91, 337–355.

    Article  Google Scholar 

  15. Ching, C.Y., Fernando, H.J.S., and Robles, A. (1995) Breakdown of line plumes in turbulent environments, J. Geophys. Res. 100, 4707–4713.

    Article  Google Scholar 

  16. Coelho, S.L.V. and Hunt, J.C.R. (1989) Vorticity dynamics of the near field of strong jets in crossflows, J. Fluid Mech. 200, 95–120, also Proc. IMA/SMAI.

    Article  Google Scholar 

  17. Csanady, G.T. (1978) Turbulent interface layers, J. Geophys. Res. 83, 2329–2342.

    Article  Google Scholar 

  18. Deardorff, J.W. and Willis, G.E. (1967) Investigation of turbulent thermal convection between horizontal plates, J. Fluid Mech. 28, 675–704.

    Article  Google Scholar 

  19. Deardorff, J.W., Willis, G.E. and Stockton, B.H. (1980) Laboratory studies of the entrainment zone of a convectively mixed layer, J. Fluid Mech. 100, 441–64.

    Article  Google Scholar 

  20. Fernando, H.J.S, Hunt, J.C.R. and Carruthers, D.J. (1994) Turbulence, waves and mixing at stratified density interfaces; modelling and experiments, in N. Rockliff and I. Castro (eds.) Proc. 4th IMA Conf. on ‘Stratified flows… ’, Clarendon, Oxford, pp. 175–200.

    Google Scholar 

  21. Frech, M. and Mahrt, L. (1995) A two scale mixing formulation for the atmospheric boundary layer, Bound. Layer Met. 23, 91–104.

    Article  Google Scholar 

  22. Frisch, U. (1996) Turbulence, Cambridge University Press, Cambridge.

    Google Scholar 

  23. Fung, J.C.H., Hunt, J.C.R.., Perkins, R.J., Wray, A.A. & Stretch, D. (1991), Defining the zonal structure of turbulence using the pressure and invariants of the deformation tensor, in A.V.Johansson and P.H. Alfredsson (eds.), Advances in Turbulence 3, Springer Verlag, Berlin, pp. 395–404.

    Chapter  Google Scholar 

  24. Gill, A. E. (1982), Atmosphere-Ocean Dynamics,Academic Press.

    Google Scholar 

  25. Gossard, E. E. and Strauch, R. G. (1983) Radar observations of clear air and clouds. Elsevier, Amsterdam.

    Google Scholar 

  26. Gregory, D. and Miller, M.J. (1989) A numerical study of deep tropical convection, Q. J. Roy. Met. Soc. 490, 1209–1241.

    Article  Google Scholar 

  27. Hewer, F.E. and Wood, N. (1997), The effective roughness length for scalar transfer in neutral conditions over hilly terrain, Quart. J. Roy. Met. Soc. (In press).

    Google Scholar 

  28. Holmes, P. J., Berkooz, G. & Lumley, J. L. (1996), Turbulence, coherent structures, symmetry and dynamical systems, Cambridge University Press, Cambridge.

    Book  Google Scholar 

  29. Hunt, J.C.R. (1984) Turbulence structure in thermal convection and shear-free boundary layers, J.Fluid Mech. 138, 161–184.

    Article  Google Scholar 

  30. Hunt, J.C.R., Kaimal, J.C. & Gaynor, J.E. (1985) Some observations of turbulence structure in stable layers, Q.J. Roy. Met. Soc. 111, 793–815.

    Article  Google Scholar 

  31. Hunt, J.C.R., Kaimal, J.C. and Gaynor, J.E. (1988) Eddy structure in the convective boundary layer — new measurements and new concepts, Q.J. Roy. Met. Soc. 114, 821–858.

    Google Scholar 

  32. Hunt, J.C.R., Moin, P., Lee, M, Moser, R.D., Spalart, P., Mansour, N.N., Kaimal, J.C. and Gaynor, E. (1989) Cross correlation and length scales in turbulent flows near surfaces, in H.-H. Fernholz and H.E. Fiedler (eds.) Advances in Turbulence 2, Springer-Verlag, Berlin, pp 128–134.

    Chapter  Google Scholar 

  33. Hunt, J.C.R., Vassilicos, J.C. & Kevlahan, N.K.R. (1994). Turbulence: a state of nature or a collection of phenomena?, in H. Branover and Y. Unger (eds.) Progress in Turbulence Research, Progress in Astronautics and Aeronautics Series vol. 162, pp. 1–18.

    Google Scholar 

  34. Hunt, J. C. R. (1995) Effects of body forces on turbulence, in R. Benzi (ed.) Advances in Turbulence V, Kluwer, pp. 229–235.

    Chapter  Google Scholar 

  35. Ruppert, H.E. (1986) The intrusion of fluid mechanics into geology, J. Fluid Mech. 173, 557–594.

    Article  Google Scholar 

  36. Ruppert, H.E. and Sparks, R.S.J. (1988) Melting the roof of a chamber containing a hot, turbulently convecting fluid, J. Fluid Mech. 188, 107–131.

    Article  Google Scholar 

  37. Jackson, P.S. (1981) On the displacement height in the logarithmic velocity profile, J. Fluid Mech. 111, 15–25.

    Article  Google Scholar 

  38. Jeong, J. Hussain, F., Schoppa, W. and Kim, J. (1997) Coherent structures near the wall in a turbulent channel flow, J. Fluid Mech. 332, 185–214.

    Google Scholar 

  39. Jimenez, J. and Moin, P (1991) The minimal flow unit in near-wall turbulence, J. Fluid Mech. 225, 213–240.

    Article  Google Scholar 

  40. Kaimal and Hougen, D.A. (1967) Characteristics of vertical velocity fluctuations observed on a 430 m. tower, Q. J. Roy. Met. Soc. 93, 305–317.

    Article  Google Scholar 

  41. Kaimal, J.C., Eversole, R.A., Lenschow, D.H., Stankov, B.B., Kahn, P.H. and Businger, J.A. (1982) Spectral characteristics of the convective boundary layer over uneven terrain, J. Atmos. Sci. 39, 1098–1114.

    Google Scholar 

  42. Keifer, J.F., Kawall, J.G., Hunt, J.C.R. and Maxey, M.R. (1978) The uniform distortion of thermal and velocity mixing layers, J. Fluid Mech. 86, 465–490.

    Article  Google Scholar 

  43. Kit, E.L.G., Strang, E.J. and Fernando, H.J.S. (1997) Measurement of turbulence near shear-free density interfaces, J. Fluid Mech. 334, 293–314.

    Article  Google Scholar 

  44. Kiya, M., Ohyama, M. and Hunt, J.C.R. (1986) Vortex pairs and rings interacting with shear layer vortices, J. Fluid Mech. 172, 1–15.

    Article  Google Scholar 

  45. Komori, S. and Nagata, K. (1996) Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification, J. Fluid Mech. 326, 205–237.

    Article  Google Scholar 

  46. Kraichnan, R. (1962) Turbulent thermal convection at arbitrary Prandtl number, Phys. Fluids 5, 1374–1389.

    Article  Google Scholar 

  47. Krettenauer, K. and Schumann, U. (1992) Numerical simulation of turbulent convection over wavy terrain, J. Fluid Mech. 237, 261–299.

    Article  Google Scholar 

  48. Krishnamurti, R. and Howard, L.N. (1981) Mean flow set up by tilted plumes in a confined space, Proc. Nat. Acad. of Sci. U.S.A. 78.

    Google Scholar 

  49. Landau, L.E. and Lifshitz, L.M. (1959) Fluid Mechanics, Pergamon, Oxford.

    Google Scholar 

  50. Lawson, R.E., Snyder, W.H., Shipman, M.S. (1998) A laboratory model of diffusion in the convective boundary layer, 10th Joint Conference on Applications of Air Pollution, American Meteorological Society, January 1998.

    Google Scholar 

  51. Lenschow, D.H. and Stephens, P.L. (1980) The role of thermals in the convective boundary layer, Bound. Layer Met. 19, 509–532.

    Article  Google Scholar 

  52. Linden, P.F. (1973) The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment, J. Fluid Mech, 60, 467–480.

    Article  Google Scholar 

  53. Linden, P.F. (1996) Natural ventilation of buildings, International Congress of Theoretical and Applied Mathematics, Kyoto.

    Google Scholar 

  54. Long, R.R. and Chen, T-C. (1981) Experimental evidence for the existence of the `mesolayer’ in turbulent systems, J. Fluid Mech. 105, 19–59.

    Article  Google Scholar 

  55. Mason, P. J. (1992) Large eddy simulation of dispersion in convective boundary layers. J. Atmos. Sci. 41, 1561–1571.

    Google Scholar 

  56. MacVean, M.K. and Mason, P.J. (1990) Cloud top entrainment instability through small scale mixing, J. Atmos. Sci. 47, 1012–1030.

    Article  Google Scholar 

  57. McGrath, J.L., Fernando, H.J.S. and Hunt, J C R (1997), Turbulence, waves and mixing at shear-free density interfaces. Part II - laboratory experiments, J. Fluid Mech. 347, 235–261.

    Article  Google Scholar 

  58. Moncrieff, M. W. (1992) Organised convective system; archetypal dynamical models, mass and momentum flux theory, and parametrization, Q. J. Roy. Met. Soc. 118, 819–850.

    Article  Google Scholar 

  59. Mory, M. (1991) A model of turbulent mixing across a density interface including the effect of rotation, J. Fluid Mech. 223, 193–207.

    Article  Google Scholar 

  60. Nieuwstadt, F.T.M. and Brost, R.A. (1986) The decay of convective turbulence, J. Atmos. Sci. 43, 532–546.

    Article  Google Scholar 

  61. Pearson, H.J., Puttock, J.S. and Hunt, J.C.R. (1983), A statistical model of particle motions and vertical diffusion in a homogeneous stratified turbulent flow, J. Fluid Mech. 129, 219–249.

    Article  Google Scholar 

  62. Perot, B. and Moin, P. (1995) Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence, J. Fluid Mech. 295, 199–227.

    Article  Google Scholar 

  63. Prandtl, L. (1932) Meteorologische Anwendung der Stromungslehre, Beitr. Phys. Atmos. 19, 188–202.

    Google Scholar 

  64. Priestley, C.H.B. (1959) Turbulent transfer in the lower atmosphere, University of Chicago Press, Chicago.

    Google Scholar 

  65. Rao, K.G., Narasimha, R. and Prabhu, A. (1996) Estimation of drag coefficient at low wind speeds over the monsoon trough land region during MONTBLEX-90, Geophys. Res. Let. 23, 2617–2620.

    Article  Google Scholar 

  66. Rodi, W. (ed.) (1982) Turbulent buoyant jets and plumes, Pergamon, Oxford.

    Google Scholar 

  67. Ruelle, D. and Takens, F. (1971) On the nature of turbulence, Commun. Math. Phys. 20, 167–192.

    Article  Google Scholar 

  68. Schmidt, H. and Schumann, U. (1989) Coherent structure of the convective boundary layer derived from large-eddy simulations, J. Fluid Mech. 200, 511–562.

    Article  Google Scholar 

  69. Schumann, U. (1996) Direct and large eddy simulation of stratified homogeneous shear flows, Dyn. Atmos. Oceans 23, 81–98.

    Article  Google Scholar 

  70. Schumann, U. and Schmidt, H. (1989) Heat transfer by thermals in the convective boundary layer, in H.H. Fernholz and H.F. Fiedler (eds.), Advances in Turbulence 2, Springer, Berlin, pp. 210–215.

    Chapter  Google Scholar 

  71. Scorer, R.S. (1954) The nature of convection as revealed by soaring birds and dragonflies, Q. J. Roy. Met. Soc. 80, 68–77.

    Article  Google Scholar 

  72. Scorer, R.S. (1978) Environmental Aerodynamics, Ellis Horwood, Chichester.

    Google Scholar 

  73. Sirovich, L. (ed.) (1991) New Perspectives in Turbulence, Springer-Verlag, Berlin.

    Google Scholar 

  74. Sparrow, E.M., Husar, R.B. and Goldstein, R. J. (1970) Observations and other characteristics of thermals, J. Fluid Mech. 41, 793–800.

    Article  Google Scholar 

  75. Strang, E. and Fernando, H.J.S. Entrainment and mixing in a stratified layer, submitted to J. Fluid Mech.

    Google Scholar 

  76. Sykes, R.I., Henn, D.I. and Lewellen, D.S. (1993) Surface layer description under free-convection conditions, Q. J. Roy. Met. Soc. 119, 409–421.

    Article  Google Scholar 

  77. Sorbjan, Z. (1997) Decay of convective turbulence revisited, Bound. Layer Met. 82, 501–515.

    Article  Google Scholar 

  78. Tennekes, H. (1975) Eulerian and Lagrangian time microscales in isotropic turbulence, J. Fluid Mech. 67, 561–567.

    Article  Google Scholar 

  79. Tennekes, H. and Lumley, J.L. (1971) First Course in Turbulence, M. I. T. Press, Cambridge, Mass.

    Google Scholar 

  80. Therry, G. and Lacarrère, P. (1983) Improving the eddy kinetic energy model for planetary boundary layer description. Bound. Layer Met. 25, 63–88.

    Article  Google Scholar 

  81. Townsend, A.A. (1959) Temperature fluctuations over a heated horizontal surface, J. Fluid Mech. 5, 209–241

    Article  Google Scholar 

  82. Townsend, A.A. (1976) The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge.

    Google Scholar 

  83. Turfus, C. and Hunt, J.C.R. (1987), A stochastic analysis of the displacements of fluid elements in inhomogeneous turbulence using Kraichnan’s method of random modes, in G. Comte-Bellot and J. Mathieu (eds.) Advances in Turbulence 1, ( Proc. European Turbulence Conf., Lyon) Springer Verlag, Berlin, pp. 191–203.

    Chapter  Google Scholar 

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

    Book  Google Scholar 

  85. Turner, J.S. (1986) Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows, J. Fluid Mech. 173, 431–471.

    Article  Google Scholar 

  86. Voropayev, S.I., Afanasyev, Y.D. and van Heist, G.J.F. (1993) Experiments on the evolution of gravitational instability of an overturned, initially stably stratified fluid, Phys. Fluid A 5, 2461–2466.

    Article  Google Scholar 

  87. Warhaft, Z. (1980) An experimental study of the effect of uniform strain on thermal fluctuations in grid-generated turbulence, J. Fluid Mech. 99, 545–573.

    Article  Google Scholar 

  88. Wong, H.Y.W. (1985) Shear free turbulence and secondary flow near angled and curved surfaces, Ph.D. Thesis, University of Cambridge.

    Google Scholar 

  89. Wyngaard, J.C. and Brost, R.A. (1984) Top-down and bottom-up diffusion in the convective boundary layer, J. Atmos. Sci. 41, 102–112.

    Article  Google Scholar 

  90. Zilitinkevich, S., Grachev, A., and Hunt J.C.R. (1998) Surface frictional processes and non-local heat/mass transfer in the shear-free convective boundary layer. See this volume.

    Google Scholar 

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Hunt, J.C.R. (1998). Eddy Dynamics and Kinematics of Convective Turbulence. In: Plate, E.J., Fedorovich, E.E., Viegas, D.X., Wyngaard, J.C. (eds) Buoyant Convection in Geophysical Flows. NATO ASI Series, vol 513. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5058-3_3

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  • DOI: https://doi.org/10.1007/978-94-011-5058-3_3

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