Journal article
Incompressible fluid turbulence at large Reynolds numbers: Theoretical basis for the t −1 decay law and the form of the longitudinal correlation function
Journal of mathematical physics, v 22(8), pp 1819-1823
Aug 1981
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Abstract
Approximately valid for large values of the time t, a formal solution to the Hopf Φ equation is obtained here as an asymptotic power series in t
−1. This approximate solution is directly applicable to grid‐generated isotropic homogeneous turbulence at large Reynolds numbers during the initial (inertial‐force dominated) period of decay; thus, the solution accounts for the observed t
−1 decay law and the fact that the longitudinal correlation function f is independent of t. It is observed that the longitudinal correlation function measured by Frenkiel, Klebanoff, and Huang is consistent with the theoretical asymptotic behavior f = (const)r
−3 as r→∞ and fitted by the expression f = [1+0.770(r/M)]−3, where M is the grid mesh length and the separation distance r is greater than the Taylor microscale (10νt)1/2. Interestingly enough, this form for the longitudinal correlation function is shown to be derivable from a variational principle.
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Details
- Title
- Incompressible fluid turbulence at large Reynolds numbers: Theoretical basis for the t −1 decay law and the form of the longitudinal correlation function
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Journal of mathematical physics, v 22(8), pp 1819-1823
- Publisher
- American Institute of Physics (AIP)
- Number of pages
- 5
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1981MF36700042
- Scopus ID
- 2-s2.0-36749120145
- Other Identifier
- 991019173630204721
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- Web of Science research areas
- Physics, Mathematical