Journal article
Transformation invariance of the longitudinal velocity correlation in grid-generated turbulence at high Reynolds numbers
Journal of fluid mechanics, v 180(1), pp 87-91
Jul 1987
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Abstract
For grid Reynolds numbers from 12800 to 81000, the Frenkiel-Klebanoff-Huang data for approximately isotropic homogeneous grid-generated turbulence shows that the longitudinal correlation function is given by the simple empirical expression f = [1 + (r/2L)]−3, where r(≥ 0.01M) is the separation distance between two points in the fluid flow and L = L(t) is the integral scale. It follows that the longitudinal velocity correlation 〈u1(x + re,t)u1(x,t)〉 = u2f with e = (1,0,0) is invariant under the separation-distance time-contraction transformations $r\rightarrow [r+(1 - \lambda)2L], t\rightarrow\lambda^{\frac{5}{2}}t$ for all positive parameter values λ ≤ 1. Conversely, if the longitudinal correlation function is prescribed to have the form f = J (r/L(t)), then the indicated transformation invariance holds if and only if [Fscr ](ξ) = (1 + ½ξ)−3. It is also shown that a Gaussian normal probability distribution at t = 0 and the Kármán-Howarth equation for all t > 0 are compatible with the transformation invariance and associated expression for f.
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Details
- Title
- Transformation invariance of the longitudinal velocity correlation in grid-generated turbulence at high Reynolds numbers
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Journal of fluid mechanics, v 180(1), pp 87-91
- Publisher
- Cambridge University Press
- Number of pages
- 5
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1987J458000004
- Scopus ID
- 2-s2.0-0023386072
- Other Identifier
- 991019174005704721
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- Web of Science research areas
- Mechanics
- Physics, Fluids & Plasmas