LOCAL ISOTROPY IN TURBULENT BOUNDARY-LAYERS AT HIGH REYNOLDS-NUMBER

To test the local-isotropy predictions of Kolmogorov's (1941) universal equilibrium theory, we have taken hot-wire measurements of the velocity fluctuations in the test-section-ceiling boundary layer of the 80 x 120 foot Full-Scale Aerodynamics Facility at NASA Ames Research Center, the world's largest wind tunnel. The maximum Reynolds numbers based on momentum thickness, R(theta), and on Taylor microscale, R(lambda), were approximately 370000 and 1450 respectively. These are the largest ever attained in laboratory boundary-layer flows. The boundary layer develops over a rough surface, but the Reynolds-stress profiles agree with canonical data sufficiently well for present purposes. Spectral and structure-function relations for isotropic turbulence were used to test the local-isotropy hypothesis, and our results have established the condition under which local isotropy can be expected. To within the accuracy of measurement, the shear-stress cospectral density E12(k1), which is the most sensitive indicator of local isotropy, fell to zero at a wavenumber about a decade larger than that at which the energy spectra first followed -5/3 power laws. At the highest Reynolds number, E12(k1) vanished about one decade before the start of the dissipation range, and it remained zero in the dissipation range. The lower wavenumber limit of locally isotropic behaviour of the shear-stress cospectra is given by k1(epsilon/S3)1/2 almost-equal-to 10 where S is the mean shear, partial derivative U/partial derivative y. The current investigation also indicates that for energy spectra this limit may be relaxed to k1(epsilon/S3)1/2 almost-equal-to 3; this is Corrsin's (1958) criterion, with the numerical value obtained from the present data. The existence of an isotropic inertial range requires that this wavenumber be much less than the wavenumber at the onset of viscous effects, k1 eta much less than 1, so that the combined condition (Corrsin 1958; Uberoi 1957), is S(nu/epsilon)1/2 much less than 1. Among other detailed results, it was observed that in the dissipation range the energy spectra had a simple exponential decay (Kraichnan 1959) with an exponent prefactor close to the value 8 = 5.2 obtained in direct numerical simulations at low Reynolds number. The inertial-range constant for the three-dimensional spectrum, C, was estimated to be 1.5+/-0.1 (Monin & Yaglom 1975). Spectral 'bumps' between the -5/3 inertial range and the dissipative range were observed on all the compensated energy spectra. The shear-stress cospectra rolled-off with a -7/3 power law before the start of local isotropy in the energy spectra, and scaled linearly with S (Lumley 1967). In summary, it is shown that one decade of inertial subrange with truly negligible shear-stress cospectral density requires S(nu/epsilon)1/2 of not more than about 0.01 (for a shear layer with turbulent kinetic energy production approximately equal to dissipation, a microscale Reynolds number of about 1500). For practical purposes many of the results of the hypothesis may be relied on at somewhat lower Reynolds numbers.