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A note on Kolmogorov's third-order structure-function law, the local isotropy hypothesis and the pressure–velocity correlation

Published online by Cambridge University Press:  26 April 2006

Erik Lindborg
Erik Lindborg
Affiliation:
Department of Mechanics, KTH, S-100 44 Stockholm, Sweden, e-mail: erikl@mech.kth.se
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Abstract

We show that Kolmogorov's (1941b) inertial-range law for the third-order structure function can be derived from a dynamical equation including pressure terms and mean flow gradient terms. A new inertial-range law, relating the two-point pressure–velocity correlation to the single-point pressure–strain tensor, is also derived. This law shows that the two-point pressure–velocity correlation, just like the third-order structure function, grows linearly with the separation distance in the inertial range. The physical meaning of both this law and Kolmogorov's law is illustrated by a Fourier analysis. An inertial-range law is also derived for the third-order velocity–enstrophy structure function of two-dimensional turbulence. It is suggested that the second-order vorticity structure function of two-dimensional turbulence is constant and scales with $\epsilon ^{2/3}_\omega$ in the enstrophy inertial range, εω being the enstrophy dissipation. Owing to the constancy of this law, it does not imply a Fourier-space inertial-range law, and therefore it is not equivalent to the k−1 law for the enstrophy spectrum, suggested by Kraichnan (1967) and Batchelor (1969).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 326 , 10 November 1996 , pp. 343 - 356
Copyright
© 1996 Cambridge University Press

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