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Statistical properties of velocity derivatives in a turbulent field

Published online by Cambridge University Press:  29 March 2006

Françlois N. Frenkiel  and
Philip S. Klebanoff
Françlois N. Frenkiel
Affiliation:
Computation and Mathematics Department, Naval Ship Research and Development Center, Washington, D.C.
Philip S. Klebanoff
Affiliation:
National Bureau of Standards, Washington, D.C.
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Abstract

High-speed digital computing methods are applied to the study of the statistical behaviour of turbulent velocity derivatives in a nearly isotropic turbulent field downstream of a grid. Higher-order correlations of turbulent velocity gradients, up to the eighth order, are measured. Contrary to the case of velocities, the higher even-order correlations of velocity gradients more clearly evidence the departure from a two-dimensional Gaussian probability distribution. Using non-Gaussian probability distribution laws the relations between different odd-and even-order correlations are obtained and compared with the experimental measurements. The conditions of similarity and isotropy are evaluated for the small-scale structure as evidenced by the behaviour of the turbulent velocity gradients. The concept of intermittency of the small-scale structure is also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 1 , 13 July 1971 , pp. 183 - 208
Copyright
© 1971 Cambridge University Press

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