The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows

Abstract

The random sweeping decorrelation hypothesis was analysed theoretically and experimentally in terms of the higher-order velocity structure functions $D_{u_i}^{(m)}(r) = \left< [u_i^m(x + r) - u_i^m(x)]^2\right>$. Measurements in two high Reynolds number laboratory shear flows were used: in the return channel (Rλ ≈ 3.2 × 103) and in the mixing layer (Rλ ≈ 2.0 × 103) of a large wind tunnel. Two velocity components (in the direction of the mean flow, u1, and in the direction of the mean shear, u2) were processed for m = 1−4. The effect of using Taylor's hypothesis was estimated by a specially developed method, and found to be insignificant. It was found that all the higher-order structure functions scale, in the inertial subrange, as r2/3. Such a scaling has been argued as supporting evidence for the sweeping hypothesis. However, our experiments also established a strong correlation between energy- and inertial-range excitation. This finding leads to the conclusion that the sweeping decorrelation hypothesis cannot be exactly valid.The hypothesis of statistical independence of large- and small-scale excitation was directly checked with conditionally averaged moments of the velocity difference $\left< [u_i(x + r) - u_i(x)]^l\right>_{u_i^*}, l = 2-4$, at a fixed value of the large-scale parameter u*i. Clear dependence of the conditionally averaged moments on the level of averaging was found. In spite of a strong correlation between the energy-containing and the inertial-scale excitation, universality of the intrinsic structure of the inertial subrange was shown.

Opportunities for use of exact statistical equations

“…Kolmogorov [18] defines local homogeneity as follows: the joint probability distribution of the velocity differences is independent of the one common spatial point, and of the velocity at the one common point, and of time. There are data [19,20,21] that contradict the statistical independence of velocity differ-ence and the velocity at either end point, and also contradict the statistical independence of velocity difference and the velocity at the midpoint. The exception is isotropic turbulence [21], for which case local homogeneity is assured.…”

Turbulence Generation from a Sweeping-Based Stochastic Model

“…Developed initially for confined subsonic jet applications, the main constraint is to take the sweeping hypothesis into account. This phenomenon, stating that inertial range structures are advected by the energy containing eddies, is identified as an important mechanism of the decorrelation process of the turbulent velocity field [2,[41][42][43]. This approach should be able to reproduce statistical properties of turbulence, such as velocity correlation functions, and to preserve the spatial distribution of the turbulent kinetic energy (TKE) imposed by the steady RANS simulation inputs.…”

“…The synthesization process of these unsteady fields is based on the sweeping hypothesis because this phenomenon is known to play a crucial role in the decorrelation process of the unsteady velocity field [2,[41][42][43]. A separation in the turbulence scales is thus required.…”

Comment on ‘The local isotropy hypothesis and the turbulent kinetic energy dissipation rate in the atmospheric surface layer’ by M. Chamecki and N. L. Dias (October B, 2004, 130, 2733–2752)

“…The simplest (with k, l = 1, 1) has been used by CD04, Katul et al (1995aKatul et al ( , 1997 and Xu et al (2001). Other higher-order correlations, with (k, l) > (1, 1), have been used by Katul et al (1995aKatul et al ( ,b, 1997, Praskovsky et al (1993) and Xu et al (2001).…”

“…The simplest (with k, l = 1, 1) has been used by CD04, Katul et al (1995aKatul et al ( , 1997 and Xu et al (2001). Other higher-order correlations, with (k, l) > (1, 1), have been used by Katul et al (1995aKatul et al ( ,b, 1997, Praskovsky et al (1993) and Xu et al (2001).Smalley and Antonia (2001) and Hill and Wilczak (2001) have argued that ρ u 1 , u 1 is an inaccurate measure of the energy-inertial scale correlation, since u 1 must contain a non-zero correlation with u 1 . Although CD04 acknowledged that Hill and Wilczak (2001) commented on the applicability of ρ u 1 , u 1 , this was misinterpreted by CD04 and they suggested that ρ u 1 , u 1 is a better means of testing for homogeneity rather than isotropy.…”