Advertisement

Introduction to Scalar and Stratified Flows

  • Carl H. Gibson
Conference paper

Abstract

Perhaps the most important practical aspect of turbulent shear flows is their dominant effect on scalar fields such as temperature, density or chemical species. When turbulence exists, it tends to completely determine the mixing and diffusion of such quantities. Industrial flows with chemical reactions, combustion, and natural flows in the ocean and atmosphere usually involve turbulence constrained by forces, and complicated by factors, that laboratory studies often suppress; for example, stratification, rotation and shear. Unstratified, nonrotating, unsheared turbulence as described by the Batchelor (1967) classic book is so complex and poorly understood that many fluid dynamicists, and most undergraduate fluid mechanics textbooks, manage to avoid the subject completely. Papers in the present chapter on Scalar and Stratified flows confront many of the awkward uncertainties attending turbulence in the “real world”. Some excellent new tools exist today that were not available to Batchelor, and their impact is reflected in the following articles.

Keywords

Internal Wave Stratify Flow Stratify Fluid Homogeneous Turbulence Turbulent Shear Flow 
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. Ashurst, W. T., Kerstein, A. R., Kerr, R. M., Gibson, C. H. (1987): Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30(8), 2343–2353ADSCrossRefGoogle Scholar
  2. Batchelor, G. K. (1967): Theory of Homogeneous Turbulence. Cambridge University PressGoogle Scholar
  3. Batchelor, G. K. (1959): Small-scale variation of convected quantities like temperature in turbulent fluid. J. Fluid Mech. 5, 113–139MathSciNetADSMATHCrossRefGoogle Scholar
  4. Dahm, W. J. A., Buch, K. A.: High resolution three-dimensional (2563) spatio-temporal measurements of the conserved scalar field in turbulent shear flows, this chapterGoogle Scholar
  5. Gargett, A. E. (1988): The scaling of turbulence in the presence of stable stratification. J. Geophys. Res. 93, 5021–5036ADSCrossRefGoogle Scholar
  6. Gerz, T., Schumann, U.: Direct simulation of homogeneous turbulence and gravity waves in sheared and unsheared stratified flows, this chapterGoogle Scholar
  7. Gibson, C. H.: Fossil Two-dimensional turbulence in the ocean, this chapterGoogle Scholar
  8. Gibson, C. H. (1980): Fossil temperature, salinity, and vorticity turbulence in the ocean. In Marine Turbulence, J. Nihoul, ed. Elsevier Publishing Co., Amsterdam, 221–257, 1980.Google Scholar
  9. Gibson, C. H. (1981): Fossil turbulence and internal waves. In American Institute of Physics Conference Proceedings No 76: Nonlinear Properties of Internal Waves, Bruce West, ed., American Institute of Physics, 159–179Google Scholar
  10. Gibson, C. H. (1988): Isoenstrophy points and surfaces in turbulent flow and mixing. Fluid Dynamics Research 3, 331–336ADSCrossRefGoogle Scholar
  11. Gibson, C. H., Ashurst, W. T., Kerstein, A. R. (1988): Mixing of strongly diffusive passive scalars like temperature by turbulence. J. Fluid Mech. 194, 261–293ADSMATHCrossRefGoogle Scholar
  12. Gibson, C. H. (1990): Scalar field topology in turbulent mixing, in Topological Fluid Mechanics, Proceedings of the IUTAM Symposium, Cambridge 1989, H. K. Moffatt and A. Tsinober (Eds.), Cambridge University Press, 85–94Google Scholar
  13. Itsweire, E. C., Heiland, K. N., Van Atta, C. W. (1986): The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 162, 299–338ADSCrossRefGoogle Scholar
  14. Melander, M. V., Hussain, F. Cut-and-connect of two antiparallel vortex tubes: a new cascade mechanism, this chapterGoogle Scholar
  15. Nagano, Y., Tagawa, M. Turbulence model for triple velocity and scalar correlations, this publication Phillips, O. M. (1969): The Dynamics of the Upper Ocean. Cambridge University PressGoogle Scholar
  16. Stillinger, D. C., Heiland, K. N., Van Atta, C. W. (1983): Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91–122ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Carl H. Gibson
    • 1
    • 2
  1. 1.Department of Applied Mechanics and Engineering SciencesUniversity of California at San DiegoLa JollaUSA
  2. 2.Department of Scripps Institution of OceanographyUniversity of California at San DiegoLa JollaUSA

Personalised recommendations