Skip to main content

Turbulence in Stratified Fluids

  • Chapter
Environmental Stratified Flows

Part of the book series: Topics in Environmental Fluid Mechanics ((EFMS,volume 3))

Abstract

Turbulence and stratification are common features of environmental flows, and their interactions lead to a myriad of flow phenomena of dynamical interest. These flow phenomena are described based on a dynamical framework provided by the equations of motion. Various broad categories of stratified turbulent flows are identified and their characteristics are briefly reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Andre, J. C., De Moor, G. Lacarrere, P., Therry, G, Du Vachat, R. Modeling the 24 hour evolution of the mean and turbulent structures of the Planetary Boundary Layer. J. Atmos. Sci. 1978; 35:1861–1883.

    Google Scholar 

  • Batchelor, G. K. The theory of homogeneous turbulence. Cambridge University Press, 1953.

    Google Scholar 

  • Batchelor, G. K. Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech., 1959; 5:113–133.

    Google Scholar 

  • Batchelor, G. K., Townsend, A. A. Decay of isotropic turbulence in the final period. Proc. R. Soc. Lond. 1948; A194:527–543.

    Google Scholar 

  • Boyer, D. L., Davies, P. A., Fernando, H. J. S., Zhang, X. Linearly stratified flow past a cylinder. Phil. Trans. R. Soc. London Ser A. 1989; 328:501–528.

    Article  Google Scholar 

  • De Silva, I. P. D., Fernando, H. J. S. Some aspects on mixing in a stratified turbulent patches. J. Fluid Mech. 1992; 240:601–625.

    Google Scholar 

  • De Silva, I. P. D., Fernando, H. J. S. Experiments on collapsing turbulent regions in stratified fluids. J. Fluid Mech. 1998; 358:29–60.

    Google Scholar 

  • De Silva, I. P. D., Fernando, H. J. S., Eaton, F., Hebert, D. Evolution of Kelvin-Helmholtz billows in nature and laboratory. Earth and Planetary Sci. Lett. 1996; 143:217–231.

    Google Scholar 

  • Deardorff, J. W. A multi-limit mixed layer entrainment formulation. J. Phys. Oceanogr. 1983; 13:988–1002.

    Article  Google Scholar 

  • Dickey, T. D., Mellor, G. L. Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 1980; 99:13–31.

    Google Scholar 

  • Fernando, H. J. S. Growth of a turbulent patch in a stratified fluid. J. Fluid Mech. 1988; 190:55–70.

    Google Scholar 

  • Fernando, H. J. S. Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech. 1991; 23:455–493.

    Article  Google Scholar 

  • Fernando, H. J. S. Aspects of stratified turbulence. Proceedings GTP workshop, Boulder, Kluwer Academic Publishing 2000 (in Press).

    Google Scholar 

  • Fernando, H. J. S., Hunt, J.C.R. Some aspects of turbulence and mixing in stably stratified fluids. Dyn. Atmos. Oceans 1996; 23:35–62.

    Article  Google Scholar 

  • Fincham, A. M., Maxworthy, T., Spedding, G. R. Energy dissipation and vortex structure in freely decaying stratified grid turbulence. Dyn. Atmos. Oceans 1996; 23(1–4):155–171.

    Google Scholar 

  • Flor, J., Fernando, H. J. S., van Heijst, G. J. F. The evolution of an isolated turbulent region in a two-layer fluid. Phys. Fluids 1994; 6(1):287–296.

    CAS  Google Scholar 

  • Fonseka, S. V., Fernando, H. J. S., van Heijst, G. J. F. Evolution of an isolated turbulent region in a stratified fluid. J. Geophys. Res. 1998; 103(C11):24857–24868.

    Article  Google Scholar 

  • Gargett, A. E., Osborn, T. R., Nasmyth, P. W. Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 1984; 144:231–280.

    Google Scholar 

  • Gerz, T., Yamazaki, H. Direct numerical simulation of buoyancy-driven turbulence in stably stratified fluid J. Fluid Mech. 1993; 249:415–440.

    CAS  Google Scholar 

  • Gibson, C. H. Fossil temperature, salinity, and vorticity turbulence in the ocean. In Marine Turbulence, J. Nihoul (ed.), Elsevier Publishing Co., Amsterdam, 1980.

    Google Scholar 

  • Gibson, C. H. Fossil turbulence and intermittency in sampling oceanic mixing processes. J. Geophys. Res, 1987; 92(C5): 5383–5404.

    Google Scholar 

  • Gibson, C. H. Laboratory, numerical, and oceanic fossil turbulence in rotating and stratified flows. J. Geophys. Res. 1991; 96:12549–12566.

    Google Scholar 

  • Gregg, M. C. Diapycnal mixing in the thermocline: A review. J. Geophys. Res. 1987; 92(C5):5249–5286.

    Google Scholar 

  • Hanazaki, H., Hunt, J. C. R. Linear processes in unsteady stably stratified turbulence. J. Fluid Mech. 1996; 318:303–337.

    CAS  Google Scholar 

  • Harris, V. G., Graham, J. A., Corrsin, S. Further experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 1977; 81:657–687.

    Google Scholar 

  • Hopfinger, E. J. Turbulence in stratified fluids: A Review. J. of Geophys. Res. 1987; 92(C5):5287–5303.

    Google Scholar 

  • Huq, P., Britter, R. E. Turbulence evolution and mixing in a two-layer stably stratified fluid. J. Fluid Mech. 1995; 285:41–67.

    Google Scholar 

  • Itsweire, E. C., Helland, K. N., van Atta, C. W. The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 1986; 162:299–338.

    Google Scholar 

  • Ivey, G. N., Nokes, R.I. Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 1989; 204:479–500.

    Google Scholar 

  • Ivey, G. N., Imberger, J. On the nature of turbulence in a stratified fluid. 1: The energetics of mixing. J. Phys. Oceanogr. 1991; 21:650–658.

    Article  Google Scholar 

  • Jacobitz, F. G., Sarkar, S. On the shear number effects in stratified shear flow. Theor. Comp. Fluid Dyn. 1999; 13:171–188.

    CAS  Google Scholar 

  • Kitaigorodskii, S. A. On the computation of the thickness of the wind mixing layer in the ocean. Bull. Acad. Sci. U.S.S.R. Geophys. Ser. 1960; 3:284–287.

    Google Scholar 

  • Lienhard, J. K., van Atta, C. W. The decay of turbulence in thermally stratified flow. J. Fluid Mech. 1990; 210:57–112.

    Google Scholar 

  • Lilly, D. K. Stratified turbulence and mesoscale variability of the atmosphere. Amer. Meteor. Soc. 1983; 40:749–761.

    Google Scholar 

  • Lin, J.-T., Pao, Y. H. Wakes in stratified fluids, Ann. Rev. Fluid Mech. 1979; 11:317.

    Article  Google Scholar 

  • Lindborg, E. Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 1998; 388:259–288.

    Google Scholar 

  • Liu, H.-T. Energetics of grid turbulence in a stably stratified fluid. J. Fluid Mech. 1995; 296:127–157.

    Google Scholar 

  • Liu, Y. N., Maxworthy, T., Spedding, G. R. Collapse of a turbulent front in a stratified fluid, 1. Nominally two-dimensional evolution in a narrow tank. J. Geophys. Res. 1987; 92(5):5427–5433.

    Google Scholar 

  • Lozovatsky, I. E., Fernando, H. J. S. Turbulent mixing on a shallow shelf, Submitted to J. Phys. Oceanogr. 2000.

    Google Scholar 

  • Mahrt, L. Stratified atmospheric boundary layers and breakdown of models. Theor. Comp. Fluid Dynamics 1998; 11:263–279.

    Google Scholar 

  • McEwan, A. D. The kinematics of stratified mixing through internal wave breaking. J. Fluid Mech. 1983; 128:47–57.

    Google Scholar 

  • Mellor, G. L., Yamada, T. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 1974; 31:1791–1806.

    Article  Google Scholar 

  • Müller, P. Small-scale vortical motions. Proceedings of the Internal Gravity Waves and Small-Scale Turbulence Hawaiian Winter Workshop, (ed. P. Muller, and R. Pujalet). Hawaii Institute of Geophysics, Honolulu. 1984.

    Google Scholar 

  • Pacanowski, R. C., Philander, S. G. H. Parameterization of vertical mixing in numerical models of tropical oceans. J. Phys. Oceanogr. 1981; 11:1442–1451.

    Article  Google Scholar 

  • Pearson, H. J., Linden, P. F. The final stage of decay of turbulence in stably stratified fluid. J. Fluid Mech. 1983; 134:195–203.

    Google Scholar 

  • Piccirillo, P.S., van Atta, C.W. The evolution of a uniformly sheared thermally stratified turbulent flow. J. Fluid Mech. 1997; 334:61–86.

    Article  Google Scholar 

  • Rehmann, C. R., Koseff, J. R. A unified scaling theory for the mixing efficiency of decaying stratified turbulence. Submitted to J. Fluid Mech., 2000.

    Google Scholar 

  • Riley, J. J., Lelong, M. P. Fluid motions in the presence of strong stable stratification. Ann. Rev. Fluid Mech. 2000; 32:613–657.

    Article  Google Scholar 

  • Riley, J. J., Metcalfe, R. W., Weissman, M. W. Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In: Nonlinear Properties of Internal Waves (ed: B.J. West). AIP Conf. Proc. 1981; 76:79–112.

    Google Scholar 

  • Rohr, J. J., Itsweire, C., Helland, K. N., van Atta, C. W. Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 1988a; 195:77–111.

    Google Scholar 

  • Rohr, J. J., Itsweire, C., Helland, K. N., van Atta, C. W. An investigation of growth of turbulence in a uniform-mean-shear flow. J. Fluid Mech. 1988b; 188:1–33.

    Google Scholar 

  • Rouse, H., Dodu, J. Turbulent diffusion across a density discontinuity. Houille Blanche 1955; 10:522–532.

    Google Scholar 

  • Sherman, F. S., Imberger, J., Corcos, G. M. Turbulence and mixing in stably stratified waters. Ann. Rev. Fluid Mech. 1978; 10:267–288.

    Article  Google Scholar 

  • Stillinger, D. C., Helland, K. N., van Atta, C. W. Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 1983; 131:91–122.

    Google Scholar 

  • Strang, E. J., Fernando, H. J. S. Entrainment and mixing in stratified shear flows. J. Fluid Mech., Submitted, 2000.

    Google Scholar 

  • Thorpe, S.A. Turbulence and mixing in a Scottish loch. Phil. Trans. Roy. Soc. London Ser. A. 1977; 286:125–181.

    Google Scholar 

  • Townsend, A. A. Structure of Turbulent Shear Flow. Cambridge University Press, 1976.

    Google Scholar 

  • Yoon, K., Warhaft, Z. The evolution of grid generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 1990; 215:601–638.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Kluwer Academic Publishers

About this chapter

Cite this chapter

Fernando, H.J.S. (2003). Turbulence in Stratified Fluids. In: Grimshaw, R. (eds) Environmental Stratified Flows. Topics in Environmental Fluid Mechanics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/0-306-48024-7_6

Download citation

  • DOI: https://doi.org/10.1007/0-306-48024-7_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-7605-7

  • Online ISBN: 978-0-306-48024-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics