278
R. A. ANTONIA AND R. E. LUXTON
10-2
(0-1
too
10'
10'
C.
1
I
0
0-6
5
10-8 I
0.06
X.
1 0 - 8 1 .
'
b
to-*
10"
coo
10'
(0'
k8
FIG. 10. Frequency spectra at x,9, = 1.42 (rough to smooth) normalized with T and :
.
(a) u component; (b) uw; (c) w' componcnt. +, zlb, ~ 0 . 1 7 ; 0 , 0.34; A, 0.68; 0, 1.02.
0. z = 0.25 cm, :/hi = 0.67. x/& = 0.35. - - - , rough wall distribution, z = 0.25 cm,
ZJS, = 0.0.16.
energy equilibrium E = T ~ / ~ / K z ;
where K is the von Kdrman constant, and
thus &(k*) = (al/~2'3)(k*)-s'3 which is independent of z as required to
collapse the spectra. In the absence of an inertial subrange this argument
does not apply and no collapse of spectra can be expectqd.
At the low wave number end of the u spactra as k* + 0,4,(&*) = @ / T ) x
( L / r ) where L is the integral length scale. In the inner e uilibrium layer L is
creases appreciably with z in that part of the layer (Bradshaw, 1967a) the low
proportional to z to a good first approximation. As t/u % , or 7 / 4 ' , also in-
R. A. ANTONIA AND R. E. LUXTON
10-2
(0-1
too
10'
10'
C.
1
I
0
0-6
5
10-8 I
0.06
X.
1 0 - 8 1 .
'
b
to-*
10"
coo
10'
(0'
k8
FIG. 10. Frequency spectra at x,9, = 1.42 (rough to smooth) normalized with T and :
.
(a) u component; (b) uw; (c) w' componcnt. +, zlb, ~ 0 . 1 7 ; 0 , 0.34; A, 0.68; 0, 1.02.
0. z = 0.25 cm, :/hi = 0.67. x/& = 0.35. - - - , rough wall distribution, z = 0.25 cm,
ZJS, = 0.0.16.
energy equilibrium E = T ~ / ~ / K z ;
where K is the von Kdrman constant, and
thus &(k*) = (al/~2'3)(k*)-s'3 which is independent of z as required to
collapse the spectra. In the absence of an inertial subrange this argument
does not apply and no collapse of spectra can be expectqd.
At the low wave number end of the u spactra as k* + 0,4,(&*) = @ / T ) x
( L / r ) where L is the integral length scale. In the inner e uilibrium layer L is
creases appreciably with z in that part of the layer (Bradshaw, 1967a) the low
proportional to z to a good first approximation. As t/u % , or 7 / 4 ' , also in-