Despite extensive study, there remain significant questions about the Reyno
lds-number scaling of the zero-pressure-gradient flat-plate turbulent bound
ary layer. While the mean how is generally accepted to follow the law of th
e wall, there is little consensus about the scaling of the Reynolds normal
stresses, except that there are Reynolds-number effects even very close to
the wall. Using a low-speed, high-Reynolds-number facility and a high-resol
ution laser-Doppler anemometer, we have measured Reynolds stresses for a ha
t-plate turbulent boundary layer from Re-theta = 1430 to 31 000. Profiles o
f (u'(2)) over bar, (v'(2)) over bar, and (u'v') over bar show reasonably g
ood collapse with Reynolds number: (u'(2)) over bar in a new scaling, and (
v'(2)) over bar and (u'v') over bar in classic inner scaling. The log law p
rovides a reasonably accurate universal profile for the mean velocity in th
e inner region.