TURBULENCE IN AN INTERNAL BOUNDARY LAYER
28 1
0
B
0
0
0
6
0.3
0
0
to-' . I 10'
10-1
100
kf
FIG. 13. Frequency spectra for rough to smooth internal layer, normalized with t and 5,.
(a) w component; (b) uw. x/5, I : 1.42: 0, z/aI = 0.34; A, 0.68; 0. 1.02.
The correlation coeficient between a narrow band of u fluctuations and
the same narrow band of w fluctuations is
and is shown in Figs. 14 and 15 for the smooth to rough htmal layer. Apart
from the low values of R,, at the station closest to the wall there is little
change in both the magnitude and shape of R,,,,, &cros~ the outer region of
the internal layer. A broad maximum value of about 0.6 is obtained at low
wave numbers. The uw spectrum a n be written as S
, = C , - iQm, where
C , , is the cospectrum and Q , is the quadrature spectrum. Note that
4,w = C,,(k*)/r and R,, = 4,,&, 4,]'/*. The coherence between the u and
112 7
R,, = ~ W ( ~ I ) / m ~ , ) )
(w (w'23
28 1
0
B
0
0
0
6
0.3
0
0
to-' . I 10'
10-1
100
kf
FIG. 13. Frequency spectra for rough to smooth internal layer, normalized with t and 5,.
(a) w component; (b) uw. x/5, I : 1.42: 0, z/aI = 0.34; A, 0.68; 0. 1.02.
The correlation coeficient between a narrow band of u fluctuations and
the same narrow band of w fluctuations is
and is shown in Figs. 14 and 15 for the smooth to rough htmal layer. Apart
from the low values of R,, at the station closest to the wall there is little
change in both the magnitude and shape of R,,,,, &cros~ the outer region of
the internal layer. A broad maximum value of about 0.6 is obtained at low
wave numbers. The uw spectrum a n be written as S
, = C , - iQm, where
C , , is the cospectrum and Q , is the quadrature spectrum. Note that
4,w = C,,(k*)/r and R,, = 4,,&, 4,]'/*. The coherence between the u and
112 7
R,, = ~ W ( ~ I ) / m ~ , ) )
(w (w'23