Fractal properties of temperature fluctuations in the convective surface layer

Abstract

Temperature fluctuations in a convective surface layer were investigated. Box counting analysis was performed to investigate fractal properties of surfaces of constant temperature and was performed on sets of points obtained by setting thresholds on detrended records. Results indicate that surfaces of constant temperature have fractal properties for thresholds far from the mean. Estimated fractal dimensions of one-dimensional cuts through these surfaces varied between 0.23 and 0.66, increasing with threshold value approaching the mean temperature. For thresholds close to the mean, no fractal behavior was found. Asymmetry in results for thresholds above and below the mean temperature was attributed to the asymmetry between updrafts and downdrafts in the convective surface layer.

The temperature dissipation rate (TD) was also investigated. It was found to be strongly intermittent with large fluctuations of the intermittency exponent. Moments were analyzed in order to investigate multifractal properties of TD. Results indicate scaling in the range of 50η–1000η (where η is the Kolmogorov scale) and multifractal properties resembling those observed for passive scalar dissipation in laboratory flows.

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

References

  1. Constantin, P., Procaccia, I., and Sreenivasan, K. R.: 1991, ‘Fractal Geometry of Isoscalar Surfaces in Turbulence: Theory and Experiments’,Phys. Rev. Lett. 67, 1739–1742.

    Google Scholar 

  2. Falconner, K.: 1990,Fractal Geometry. Mathematical Foundations and Applications, John Wiley & Sons, Chichester.

    Google Scholar 

  3. Feder, J.: 1988,Fractals, Plenum Press, New York.

    Google Scholar 

  4. Hentschel, H. G. E. and Procaccia, I.: 1983, ‘The Infinite Number of Generalized Dimensions of Fractals and Strange Attractors’,Physica,D 8, 435–444.

    Google Scholar 

  5. Hentschel, H. G. E. and Procaccia, I.: 1984, ‘Relative Diffusion in Turbulent Media: The Fractal Dimension of Clouds’,Phys. Rev. A,28, 1461–1470.

    Google Scholar 

  6. Lovejoy, S.: 1982, ‘Area-Perimeter Relation for Rain and Cloud Areas’,Science 216, 185–187.

    Google Scholar 

  7. Malinowski, S. P. and Zawadzki, I.: 1993, ‘On the Surface of Clouds’,J. Atmos. Sci. 50, 5–13.

    Google Scholar 

  8. Malinowski, S. P., Leclerc, M. Y., and Baumgardner, D.: 1994, ‘Fractal Analysis of High Resolution Cloud Droplet Measurements’,J. Atmos. Sci. 51, (3), 397–413.

    Google Scholar 

  9. Mandelbrot, B. B.: 1974, ‘Intermittent Turbulence in Self-Similar Cascades: Divergence of High Moments and Dimension of the Carrier’,J Fluid. Mech. 62, part 2, 331–358.

    Google Scholar 

  10. Mandelbrot, B. B.: 1989, ‘Multifractal Measures, Especially for the Geophysicist’,Pure Appl. Geophys. 131, 6–42.

    Google Scholar 

  11. Meneveau, C. and Sreenivasan, K. R.: 1991, ‘The Multifractal Nature of Turbulent Energy Dissipation’,J. Fluid. Mech. 224, 428–484.

    Google Scholar 

  12. Miller, P. L. and Dimotakis, P. E.: 1991, ‘Stochastic Geometric Properties of Scalar Interfaces in Turbulent Jets’,Phys. Fluids A,3 (1), 168–177.

    Google Scholar 

  13. Prasad, R. R., Meneveau, C., and Sreenivasan, K. R.: 1988, ‘Multifractal Nature of the Dissipation Field of Passive Scalars in Fully Turbulent Flows’,Phys. Rev. Lett. 61, 74–77.

    Google Scholar 

  14. Prasad, R. R. and Sreenivasan, K. R.: 1990, ‘Multifractal Nature of the Dissipation Field of Passive Scalars in Fully Turbulent Flows’,J. Fluid. Mech. 216, 1–34.

    Google Scholar 

  15. Saucier, A.: 1991, ‘Cascade Process and Fully Developed Turbulence’, Ph.D. thesis, Department of Physics, McGill University, Montreal, Canada, January 1991.

    Google Scholar 

  16. Schertzer, D. and Lovejoy, S.: 1989, ‘Generalised Scale Invariance and Multiplicative Process in the Atmosphere’,Pure Appl. Geophys. 131, 57–81.

    Google Scholar 

  17. Sreenivasan, K. R.: 1991, ‘Fractals and Multifractals in Fluid Turbulence’,Annu. Rev. Fluid Mech. 23, 539–600.

    Google Scholar 

  18. Sreenivasan, K. R., Ramshankar, R., and Meneveau, C.: 1989, ‘Mixing, Entrainment and Fractal Dimensions of Surfaces in Turbulent Flows’,Proc. R. Soc. Lond, A,421, 79–108.

    Google Scholar 

  19. Turner, J. S.: 1986, ‘Turbulent Entrainment: The Development of the Entrainment Assumption, and its Application to Geophysical Flows’,J. Fluid Mech. 173, 431–471.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Malinowski, S.P., Leclerc, M.Y. Fractal properties of temperature fluctuations in the convective surface layer. Boundary-Layer Meteorol 71, 169–187 (1994). https://doi.org/10.1007/BF00709225

Download citation

Keywords

  • Surface Layer
  • Constant Temperature
  • Fractal Property
  • Dissipation Rate
  • Temperature Fluctuation