276
R. A. ANTONIA AND R. E. LUXTON
lo-' I I "
FIG. 8. Frequency spectra at x/6, = 2.10 (smooth to rough) normalized with T and i .
(a) u component; (h) w coinpornat; (c) w . 0, z/6, = 0.29; A, 0.58; + ,037; 0 , 1.16;
V, 2.32.
In a fully developed nearly self-preserviw boundary layer with zero pressure gradient on either a smooth or a rough wall, where advection and
diffusion terms are small, the "active" and uhactivc" motion ideas and the
associated r''2, z scaling should be dfective in collapsing spectra. A sample
of such spectra for the u component obtained in the inner region (y/6 < 0.25
approximately) of the nearly self-preserving smooth and rough wall layers is
shown in Fig. 11. The changes in spectral shape with increasing distance
from the wall are the same as t h w reveakd in Figs. 8-10 for the nonequilibrium interml layers. KlebanofF's (1955) data and the densities 4, and + ,
, ,
not shown here, also exhibit the same trends. The failure of these data to
collapse on r, z scaling as effectively as the data from the two equilibrium
layers in adverse pressure gradients measured by Bradshaw (1967b)