The anisotropy of the small scale structure in high Reynolds number (Rλ∼1000) turbulent shear flow

Abstract

The postulate of local isotropy (PLI) is tested in a wind tunnel uniform shear flow in which the Reynolds number is varied over the range 100⩽Rλ⩽1, 100(6.7×102⩽Rl⩽6.3×104). The high Rλ is achieved by using an active grid [Mydlarski and Warhaft, J. Fluid Mech. 320, 331 (1996)] in conjunction with a shear generator. We focus on the increments of the longitudinal velocity fluctuations in the direction of the mean shear. PLI requires that odd order moments of these quantities approach zero as Rλ→∞. Confirming the lower Reynolds number measurements of Garg and Warhaft [Phys. Fluids 10, 662 (1998)], we show that the skewness of ∂u/∂y decreases as Rλ−0.5 (with a value of 0.2 at Rλ∼1000). Although the decrease is slower than classical scaling arguments suggest, the result is consistent with PLI, indicating a negligible value at high Rλ. However, the normalized fifth moment, 〈(∂u/∂y)5〉/〈(∂u/∂y)2〉5/2, is of order 10, and shows no diminution with Reynolds number, while the normalized seventh moment increases with Rλ. These dissipation range results are inconsistent with PLI. Within the inertial subrange we show that all the odd order moments of the increments of Δu(y) are nonzero, exhibiting scaling ranges. Here, the skewness structure function has a value ∼0.5 indicating that in the inertial subrange significant anisotropy is evident even at the third moment level. Fifth- and seventh-order inertial subrange skewness structure functions are of order 10 and 100, respectively. The results show that PLI is untenable, both at dissipation and inertial scales, at least to Rλ∼1000, and suggest it is unlikely to be so even at higher Reynolds numbers.

Fluid particle accelerations in fully developed turbulence

“…The anisotropy is large at low Reynolds number and diminishes to a small value at R λ = 970. This observation tends to confirm recent experimental results which indicate that anisotropy may persist to much higher Reynolds numbers than previously believed [19,20].In summary, our measurements indicate that the Heisenberg-Yaglom scaling of acceleration variance is observed for 500 ≤ R λ ≤ 970. At lower Reynolds number, our measurements are consistent with the anomalous scaling observed in DNS [14,16].…”

Dynamics of POD Modes in Wall Bounded Turbulent Flow

“…Third-order transverse structure functions of the longitudinal velocity were found to have a scaling range, showing the existence of anisotropy at both inertial and dissipation scales. Shen & Warhaft [4] continued the experiments. They showed that the fifth moment of the derivative of the longitudinal fluctuation in the direction of the mean gradient, is of order 10 with no diminution with the Reynolds number.…”

The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

“…At the same time it was found that lateral structure functions D n (r) = <[u(x,y,z+r) -u(x,y,z)] n > of odd orders n = 3, 5, and 7 take non-zero values in the inertial range of lengths r (i.e., for TJ «r « L); hence the studied homogeneous-shear-flow turbulence is anisotropic also in the inertial range of lengths. Thus, results of [127] show that the shear-flow turbulence is locally non-isotropic, at least to Re x ~ 1000, and demonstrates no tendency to become isotropic at higher values of Re v Here again the question arises how the discovered local anisotropy can be combined with the validity of the ordinary laws of two and five thirds which was confirmed by data relating to very different high-Reynolds-number shear flows. Strong deviations from the predictions of K41 theory were in fact first detected in studies of small-scale fluctuations of temperature (or other passive scalars) in high-Reynolds-number turbulent flows.…”

“…Their measurements in the atmospheric surface layer at 10 4 < Re x < 2xl0 4 led them to the conclusion that apparently in atmospheric turbulence there exists an inertial range where Eq. (17) is valid but its validity is often disturbed by velocity shear and finiteness of Re (see also the discussion of the results of the paper [127] below). However, the paper [122] did not clarify the origin of the similarity law (17).…”

“…In addition to this, Shen and Warhaft [127] measured recently a number of small-scale characteristics of velocity fluctuations in a homogeneous shear flow (with constant shear dU/dz where U is the mean velocity) behind an active grid. These measurements covered the range 100 < Re^<1100 of high enough Reynolds numbers Re v For the normalized moments of streamwise-velocity derivative 3u/9z (20) they found that S 3 is decreasing with Re^ (and possibly tends to zero as Re x -»<*>), while S 5 does not decrease with Re x (and is close to 10 at R& x~ 1000), while S 7 increases with Re x .…”