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Turbulence in stably stratified fluids: A review of laboratory experiments

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Abstract

This is a review of laboratory studies of mixing in stably stratified fluids away from the direct intluence of boundary layers, and was written to introduce the session on laboratory experiments at the IUCRM Colloquium.

Internal waves (Section 2) can lead to turbulence by creating regions of unstable density gradients through their mutual interactions, by individually breaking by forming rotors, and by reducing the local Richardson number until Kelvin-Helmholtz instability results. They may be important in radiating energy from turbulent or spreading regions. Critical-layer absorption of internal waves is not found to be a direct cause of turbulence in experiments with 15⩾ Richardson number ⩾5, although the modification of the vertical density profile may be significant.

Turbulent-laminar interfaces without mean shear (Section 3) and with mean shear (Section 4) are described. The source of turbulence in these experiments is partly external, either generated by an oscillating grid or by a (relatively) moving boundary. The development of turbulence generated entirelywithin a stratified layer by Kelvin-Helmholtz instability, is described in detail in Section 5, and the results are compared with measurements in the ocean and in the atmosphere.

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References

  • Arya, S. P. S.: 1972, ‘The Critical Condition for the Maintenance of Turbulence in Stratified Flows’,Quart. J. Roy. Meteorol. Soc. 98, 264–273.

    Article  Google Scholar 

  • Badgley, F. I.: 1969, ‘Large Scale Processes Contributing Energy to Clear Air Turbulence’, in Y.-H. Pao and A. Goldberg (eds.),Clear Air Turbulence and its Dectection, Plenum Press, New York, pp. 109–123.

    Google Scholar 

  • Benjamin, T. B.: 1967, ‘Internal Waves of Permanent Form in Fluids of Great Depth’,J. Fluid Mech. 29, 559–592.

    Article  Google Scholar 

  • Benjamin, T. B.: 1968, ‘Gravity Currents and Related Phenomena’,J. Fluid Mech. 31, 209–248.

    Article  Google Scholar 

  • Booker, J. R. and Bretherton, F. P.: 1967, ‘The Critical Layer for Internal Gravity Waves in a Shear Flow’,J. Fluid Mech. 27, 513–539.

    Article  Google Scholar 

  • Breeding, R. J.: 1971, ‘A Non-Linear Investigation of Critical Levels for Internal Atmospheric Gravity Waves’,J. Fluid Mech. 50, 545–564.

    Article  Google Scholar 

  • Bretherton, F. P., Hazel, P., Thorpe, S. A., and Woods, I.: 1967,J. Fluid Mech. 30, 781–784 (appendix to a paper by P. Hazel).

    Google Scholar 

  • Browning, K. A.: 1971, ‘Structure of the Atmosphere in the Vicinity of Large-Amplitude Kelvin-Helmholtz Billows’,Quart. J. Roy. Meteorol. Soc. 97, 283–299.

    Google Scholar 

  • Browning, K. A. and Watkins, C. D.: 1970, ‘Observations of Clear Air Turbulence by High Power Radar’, Nature227, 260–263.

    Article  Google Scholar 

  • Cermak, J. E. and Arya, S. P. S.: 1970, ‘Problems of Atmospheric Shear Flows and Their Laboratory Simulation’,Boundary-Layer Meteorol. 1, 40–60.

    Article  Google Scholar 

  • Davis, R. E.: 1969, ‘The Two-Dimensional Flow of a Stratified Fluid over an Obstacle’,J. Fluid Mech. 36, 127–144.

    Article  Google Scholar 

  • Davis, R. E. and Acrivos, A.: 1967a, ‘The Stability of Oscillating Internal Waves’,J. Fluid Mech. 30, 723–736.

    Article  Google Scholar 

  • Davis, R. E. and Acrivos, A.: 1967b, ‘Solitary Internal Waves in Deep Water’,J. Fluid Mech. 29, 593–607.

    Article  Google Scholar 

  • Dutton, J. A.: 1969, ‘An Energy Budget for a Layer of Stratospheric C.A.T.’,Radio Sci. 4, 1137–1142.

    Article  Google Scholar 

  • Ellison, T. H. and Turner, J. S.: 1959, ‘Turbulent Entrainment in Stratified Flows’,J. Fluid Mech. 6, 423–448.

    Article  Google Scholar 

  • Görtler, H.: 1943, ‘Uber eine Schwingungserscheinung in Flüssigkeiten mit stabiler Dichteschichtung’,Z. Angew. Math. Mech. 23, 65–71.

    Article  Google Scholar 

  • Grant, H. L., Moilliet, A., and Vogel, W. M.: 1968, ‘Some Observations of the Occurrence of Turbulence in and Above the Thermocline’,J. Fluid Mech. 34, 443–448.

    Article  Google Scholar 

  • Hazel, P.: 1972, ‘Numerical Studies of the Stability of Inviscid Stratified Shear Flows’,J. Fluid Mech. 51, 39–62.

    Article  Google Scholar 

  • Kato, H. and Phillips, O. M.: 1969, ‘On the Penetration of a Turbulent Layer Into a Stratified Fluid’,J. Fluid Mech. 37, 643–655.

    Article  Google Scholar 

  • Keulegan, G. H. and Carpenter, L. H.: 1961, ‘An Experimental Study of Internal Progressive Oscillatory Waves’, unpublished report.

  • Lofquist, K.: 1960, ‘Flow and Stress Near an Interface Between Stratified Fluids’,Phys. Fluids,3, 158–177.

    Article  Google Scholar 

  • Long, R. R.: 1953, ‘Some Aspects of the Flow of Stratified Fluids’,Tellus 5, 42–58.

    Article  Google Scholar 

  • Martin, S., Simmons, W. F., and Wunsch, C.: 1969, ‘Resonant Internal Wave Interaction’,Nature 224, 1014–1015.

    Article  Google Scholar 

  • Mather, G. K.: 1971, ‘Flight Studies of Clear Air Turbulence — The Current Position and Further Research Needs’, inProceedings of the International Conference on Atmospheric Turbulence, Royal Aero Soc., London.

    Google Scholar 

  • McEwan, A. D.: 1971, ‘Degeneration of Resonantly-Excited Standing Internal Gravity Waves’,J. Fluid Mech. 50, 431–448.

    Article  Google Scholar 

  • Moore, M. J. and Long, R. R.: 1971, ‘An Experimental Investigation of Turbulent Stratified Shearing Flow’,J. Fluid Mech. 49, 635–655.

    Article  Google Scholar 

  • Mowbray, D. E. and Rarity, B. S.H.: 1967, ‘A Theoretical and Experimental Investigation of the Phase Configuration of Internal Waves of Small Amplitude in a Density Stratified Liquid’,J. Fluid Mech. 28, 1–16.

    Article  Google Scholar 

  • Ozmidov, R. V.: 1965, ‘On the Turbulent Exchange in a Stably Stratified Ocean’,Zzv. Atm. Ocean Phys. 1, 853–860.

    Google Scholar 

  • Pao, Y.-H.: 1969, ‘Origin and Structure of Turbulence in Stably Stratitied Media’, in Y.-H. Pao and A. Goldburg (eds.),Clear Air Turbulence and its Detection, Plenum Press, N. Y., pp. 73–99.

    Google Scholar 

  • Rouse, H. and Dodu, J.: 1955, ‘Diffusion Turbulente à travers une discontinuité de densitt’,La Houille Blanche 4, 522–532.

    Article  Google Scholar 

  • Schooley, A. H. and Stewart, R. W.: 1963, ‘Experiments with a Self-Propelled Body in a Stratified Fluid’,J. Fluid Mech. 9, 83–96.

    Article  Google Scholar 

  • Scotti, R. S. and Corcos, G. M.: 1969, ‘Measurements of the Growth of Small Disturbances in a Stratified Shear Layer’,Radio Sci. 4, 1309–1314.

    Article  Google Scholar 

  • Thorpe, S. A.: 1968, ‘A Method of Producing a Shear Flow in a Stratified Fluid’,J. Fluid Mech. 32, 693–704.

    Article  Google Scholar 

  • Thorpe, S. A.: 1969a, ‘Experiments on the Stability of Stratified Shear Flows’,Radio Sci. 4, 1327–1332.

    Article  Google Scholar 

  • Thorpe, S. A.: 1969b, ‘On the Shape of Progressive Internal Waves’,Phil. Trans. Roy. Soc. A263, 563–614.

    Google Scholar 

  • Thorpe, S. A.: 1971a, ‘Experiments on the Instability of Stratified Shear Flows: Miscible Fluids’,J. Fluid Mech. 46, 299–320.

    Article  Google Scholar 

  • Thorpe, S. A.: 1971b, ‘Kelvin-Helmholtz Instability and Turbulence’, inProceedings of the Znternational Conference on Atmospheric Turbulence, Roy. Aero. Soc., London.

    Google Scholar 

  • Townsend, A. A.: 1958, ‘Turbulent Flow in a Stably Stratified Atmosphere’,J. Fluid Mech. 3, 361–372.

    Article  Google Scholar 

  • Townsend, A. A.: 1964, ‘Natural Convection in Water Over an Ice Surface’,Quart. J. R. Meteorol. Soc. 90, 248–259.

    Article  Google Scholar 

  • Townsend, A. A.: 1965, ‘Excitation of Internal Waves by a Turbulent Boundary Layer’,J. Fluid Mech. 22, 241–252.

    Article  Google Scholar 

  • Townsend, A. A.: 1968, ‘Excitation of Internal Waves in a Stably-Stratified Atmosphere with Considerable Wind Shear’,J. Fluid Mech. 32, 145–171.

    Article  Google Scholar 

  • Turner, J. S.: 1968, ‘The Influence of Molecular Diffusivity on Turbulent Entrainment Across a Density Interface’,J. Fluid Mech. 33, 639–656.

    Article  Google Scholar 

  • Turner, J. S.: 1973,Buoyancy Effkcts in Fluids, to be published by Cambridge University Press.

  • Woods, J. D. and Wiley, R. L.: 1972, ‘Billow Turbulence and Ocean Microstructure’,Deep-Sea Res. 19, 87–121.

    Google Scholar 

  • Wu, J.: 1969, ‘Mixed Region Collapse with Internal Wave Generation in a Density Stratified Medium’,J. Fluid Mech. 35, 531–544.

    Article  Google Scholar 

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Thorpe, S.A. Turbulence in stably stratified fluids: A review of laboratory experiments. Boundary-Layer Meteorol 5, 95–119 (1973). https://doi.org/10.1007/BF02188314

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