On the onset of high-Reynolds-number grid-generated wind tunnel turbulence

Using an active grid devised by Makita (1991), shearless decaying turbulence is studied for the Taylor-microscale Reynolds number, R(lambda), varying from 50 to 473 in a small (40 x 40 cm(2) cross-section) wind tunnel. The turbulence generator consists of grid bars with triangular wings that rotate and flap in a random way. The value of R(lambda) is determined by the mean speed of the air (varied from 3 to 14 m s(-1)) as it passes the rotating grid, and to a lesser extent by the randomness and rotation rate of the grid bars. Our main findings are as follows. A weak, not particularly well-defined scaling range (i.e. a power-law dependence of both the longitudinal (u) and transverse (nu) spectra, F-11(k(1)) and F-22(k(1)) respectively, on wavenumber k(1)) first appears at R(lambda) similar to 50, with a slope, n(1), (for the u spectrum) of approximately 1.3. As R(lambda) was increased, n(1) increased rapidly until R(lambda) similar to 200 where n similar to 1.5. From there on the increase in n(1) was slow and even by R(lambda) = 473 it was still significantly below the Kolmogorov value of 1.67. Over the entire range, 50 less than or equal to R(lambda) less than or equal to 473, the data were well described by the empirical fit: n(1) = 5/3(1-3.15R(lambda)(-2/3)). Using a modified form of the Kolmogorov similarity law: F-11(k(1)) = C-1*epsilon(2/3)k(1)(-5/3)(k(1) eta)(5/3-n1) where epsilon is the turbulence energy dissipation rate and eta is the Kolmogorov microscale, we determined a linear dependence between n(1) and C-1*: C-1* = 4.5-2.4 n(1). Thus for n(1) = 5/3 (which extrapolation of our results suggests will occur in this flow for R(lambda) similar to 10(4)), C-1* = 0.5, the accepted high-Reynolds-number value of the Kolmogorov constant. Analysis of the p.d.f. of velocity differences Delta u(r) and Delta v(r) where r is an inertial subrange interval, conditional dissipation, and other statistics showed that there was a qualitative difference between the turbulence for R(lambda) < 100 (which we call weak turbulence) and that for R(lambda) > 200 (strong turbulence). For the latter, the p.d.f.s of Delta u(r) and Delta v(r) had super Gaussian tails and the dissipation (both of the u and nu components) conditioned on Delta u(r) and Delta v(r) was a strong function of the velocity difference. For R(lambda) < 100, p.d.f.s of Delta u(r) and Delta v(r) were Gaussian and conditional dissipation statistics were weak. Our results for R(lambda) > 200 are consistent with the predictions of the Kolmogorov refined similarity hypothesis (and make a distinction between the dynamical and kinematical contributions to the conditional statistics). They have much in common with similar statistics done in shear flows at much higher R(lambda), with which they are compared.