Journal article
Incompressible Fluid Turbulence at Large Reynolds Numbers: Theoretical Basis for the t super(-1) Decay Law and the Form of the Longitudinal Correlation Function
J. MATH. PHYS, Vol.22(8), pp.1819-1823
01 Jan 1981
Abstract
Approximately valid for large values of the time t, a formal solution to the Hopf Phi equation is obtained here as an asymptotic power series in t super(-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 super(-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 super(-3) as r arrow right infinity and fitted by the expression f = (1 + 0.770(r/M)) super(-3), where M is the grid mesh length and the separation distance r is greater than the Taylor microscale (10vt) super(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 super(-1) Decay Law and the Form of the Longitudinal Correlation Function
- Creators
- G Rosen
- Publication Details
- J. MATH. PHYS, Vol.22(8), pp.1819-1823
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Identifiers
- 991020705439504721