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

To test the local-isotropy predictions of Kolmogorov's (1941) universa l equilibrium theory, we have taken hot-wire measurements of the veloc ity fluctuations in the test-section-ceiling boundary layer of the 80 x 120 foot Full-Scale Aerodynamics Facility at NASA Ames Research Cent er, the world's largest wind tunnel. The maximum Reynolds numbers base d on momentum thickness, R(theta), and on Taylor microscale, R(lambda) , were approximately 370000 and 1450 respectively. These are the large st ever attained in laboratory boundary-layer flows. The boundary laye r develops over a rough surface, but the Reynolds-stress profiles agre e with canonical data sufficiently well for present purposes. Spectral and structure-function relations for isotropic turbulence were used t o test the local-isotropy hypothesis, and our results have established the condition under which local isotropy can be expected. To within t he accuracy of measurement, the shear-stress cospectral density E12(k1 ), which is the most sensitive indicator of local isotropy, fell to ze ro at a wavenumber about a decade larger than that at which the energy spectra first followed -5/3 power laws. At the highest Reynolds numbe r, E12(k1) vanished about one decade before the start of the dissipati on range, and it remained zero in the dissipation range. The lower wav enumber limit of locally isotropic behaviour of the shear-stress cospe ctra is given by k1(epsilon/S3)1/2 almost-equal-to 10 where S is the m ean shear, partial derivative U/partial derivative y. The current inve stigation also indicates that for energy spectra this limit may be rel axed 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. Th e existence of an isotropic inertial range requires that this wavenumb er be much less than the wavenumber at the onset of viscous effects, k 1 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 detail ed results, it was observed that in the dissipation range the energy s pectra had a simple exponential decay (Kraichnan 1959) with an exponen t prefactor close to the value 8 = 5.2 obtained in direct numerical si mulations 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 t he start of local isotropy in the energy spectra, and scaled linearly with S (Lumley 1967). In summary, it is shown that one decade of inert ial subrange with truly negligible shear-stress cospectral density req uires S(nu/epsilon)1/2 of not more than about 0.01 (for a shear layer with turbulent kinetic energy production approximately equal to dissip ation, a microscale Reynolds number of about 1500). For practical purp oses many of the results of the hypothesis may be relied on at somewha t lower Reynolds numbers.