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Fractal properties of inertial-range turbulence with implications for aircraft response

Published online by Cambridge University Press:  04 July 2016

J. G. Jones ,
G. W. Foster  and
A. Haynes
J. G. Jones
Affiliation:
Royal Aerospace Establishment, Farnborough
G. W. Foster
Affiliation:
Royal Aerospace Establishment, Bedford
A. Haynes
Affiliation:
Royal Aerospace Establishment, Bedford
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Summary

Fractal geometry provides a method for modelling the scale dependence of fluctuations in atmospheric-turbulence velocity. In this paper the basic concepts are outlined and illustrated by a method of data analysis which, for a fractal process, displays measured probability distributions in scale-invariant form. To a first approximation the data exhibit statistical self-similarity, consistent with the classical theory of Kolmogorov. However, on more detailed analysis, the more intense fluctuations show systematic departures from self-similarity, consistent with recent theoretical estimates of the fractal dimension of the support of turbulence. Implications for aircraft gust response are discussed.

Type
Research Article
Information
The Aeronautical Journal , Volume 92 , Issue 918 , October 1988 , pp. 301 - 308
Copyright
Copyright © Royal Aeronautical Society 1988 

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References

1. Kolmogorov, A. N. Local structure of turbulence in an incompressible liquid for very large Reynolds numbers. Comptes Rendus (Dokl) Acad Sci URSS, 1941, 30, 299–303.Google Scholar
2. Kolmogorov, A. N. Refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech, 1962, 13, 82–85.Google Scholar
3. Oboukhov, A. M. Some specific features of atmospheric turbulence. J Fluid Mech, 1962, 13, 77–81.Google Scholar
4. Jones, J. G. Modelling of gusts and wind shear for aircraft assessment and certification. Proc Indian Acad Sci (Eng Sci), 1980, 3, 1–30.Google Scholar
5. Van Atta, C. W. and Park, J. Statistical self-similarity and inertial subrange turbulence. In: Rosenblatt, M. and Van Atta, C. W. (eds), Statistical Models and Turbulence, Springer, Berlin, 1972, 402–426.Google Scholar
6. Mandelbrot, B. The Fractal Geometry of Nature. Freeman, San Francisco, 1982.Google Scholar
7. Lovejoy, S. and Schertzer, D. Generalized scale invariance in the atmosphere and fractal models of rain. Water Resources Res August 1985, 21, (8), 1233–1250.Google Scholar
8. Frisch, U., Sulem, P.-L. and Nelkin, M. A simple dynamical model of intermittent fully developed turbulence. J Fluid Mech, 1978, 87, 719–736.Google Scholar
9. Jones, J. G. and Haynes, A. A peakspotter program applied to the analysis of increments in turbulence velocity. Royal Aircraft Establishment Technical Report 84071, 1984.Google Scholar
10. Foster, G. W. Results of low altitude atmospheric turbulence measurements by Gnat XP505. Royal Aircraft Establishment Technical Report 87015, 1987.Google Scholar
11. Jones, J. G. and Foster, G. W. Paper in preparation.Google Scholar
12. Jones, J. G. On self-similarity, fractal dimension and aircraft response to gusts. Royal Aircraft Establishment Technical Memorandum FS244, 1979.Google Scholar
13. Parisi, O. and Frisch, U. A multifractal model of intermittency. In: Ghil, M., Benzi, R. and Parisi, O. (eds). Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, Nofth-Holland, Amsterdam, 1985, 84–88.Google Scholar
14. Jones, J. G. and Fry, D. E. Aircraft ride-bumpiness and the design of ride-smoothing systems. AGARD Conference Proceedings CP-240, 1977.Google Scholar
15. Houbolt, J. C. The art of determining gust frequency response functions. 31st AGARD Structures and Materials Panel Meeting, Norway, 1970.Google Scholar