A rigorous mathematical description is given for the physical concept of the cascade process of sequential breakdown of turbulent eddies. It is assumed that the probability distribution for the ratio of typical values of turbulent fluctuations averaged over a small volume v to those averaged over a surrounding larger volume V is invariant under the group of space similarity transformations, provided that the length scales of both volumes are much smaller than the external scale of turbulence and much larger than the Kolmogoroff scale. This assumption is in general agreement with the conclusions of Kolmogoroff and Obukhov and with the existing measurements of the power spectrum for the square of the velocity derivative. Some measurements of probability distributions for smallscale turbulent fluctuations are also discussed.
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September 1967
Research Article|
September 01 1967
Breakdown of Eddies and Probability Distributions for Small‐Scale Turbulence
A. S. Gurvich;
A. S. Gurvich
Institute of Atmospheric Physics, Academy of Sciences of the USSR, Moscow, USSR
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A. M. Yaglom
A. M. Yaglom
Institute of Atmospheric Physics, Academy of Sciences of the USSR, Moscow, USSR
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A. S. Gurvich
A. M. Yaglom
Institute of Atmospheric Physics, Academy of Sciences of the USSR, Moscow, USSR
Phys. Fluids 10, S59–S65 (1967)
Citation
A. S. Gurvich, A. M. Yaglom; Breakdown of Eddies and Probability Distributions for Small‐Scale Turbulence. Phys. Fluids 1 September 1967; 10 (9): S59–S65. https://doi.org/10.1063/1.1762505
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