'TRANSIWRT MODEL I,IMITATIONS IN TURBULENCE
45
lo the boundary layer region between 0.2b and 0.458. an estimate of the
mean velocity gradient difference over a distance L, gives
a 70 ?, , difference in mean gradient over one characteristic transport scale!
Although this is rather large, the operant dimensionless criterion analogous
to Eq. (13) is
(62 )
lC'zzz/Liz 1 (L$/24) -4 1.
At z,'S = 0.2 and 0.45. this number is 0.12 a i d 0.04, respectively. We conclude that in the outer part of the boundary layer, this condition is well
satisfied.
There may be regions in some meteorological or oceanographic flows
which also fulfill this condition.
In recent years there has been a systematic effort to generate laboratory
flows which satisfy Eq. (13) over relatively large distances (Wiskind, 1962;
Rose, 1966; Champagne et a/., 1970). It is hoped that these experiments will
gradually be generalized to include small amounts of mean gradient
variation.
It is, of course, much easier to postulate a homogeneous turbulent transport situation (e.g., Corrsin, 1952; Reis, 1952; Burgers and Mitchner,
1953a,b; Craya, 1958; Deissler, 1961; Fox, 1964; Courseau and Loiseau,
1972a.b) than to generate it in the laboratory.
We can supplement the meanfield homogeneity condition which relates to
condition (a) above with a look at the meanfield time stationarity condition,
which is a kind of time scale limitation, condition (b). With momentum
transport time scale T, already estimated for a turbulent boundary layer, we
can ask whether the mean velocity gradient changes appreciably in this time
interval, observing in the convected frame. The analog of Eq. (20) is
(63)
l%a I ( T l 4 6 1 Or I W L 1 (T,/2) 4 1
in the convected frame. Estimating just the first of these from the
Blackwelder/Kovasznay data, we find 0.005 and 0.009 at : / a = 0.20 and
0.45, respectively. Condition (63) is well satisfied.
The third and fourth conditions [(c) and (d)] listed at the start of this
scction specify hornogencity of the length and velocity which characterize
the transport mechanism itself. We look at the boundary layer data for T,
and w' variations between zlb; = 0.20 and 0.45; from the data of Kovasznay
P/ ( I / . (1970). and of Blackwelder and Kovasznay and of Klebanoff, we can
cstiniate Table I.
45
lo the boundary layer region between 0.2b and 0.458. an estimate of the
mean velocity gradient difference over a distance L, gives
a 70 ?, , difference in mean gradient over one characteristic transport scale!
Although this is rather large, the operant dimensionless criterion analogous
to Eq. (13) is
(62 )
lC'zzz/Liz 1 (L$/24) -4 1.
At z,'S = 0.2 and 0.45. this number is 0.12 a i d 0.04, respectively. We conclude that in the outer part of the boundary layer, this condition is well
satisfied.
There may be regions in some meteorological or oceanographic flows
which also fulfill this condition.
In recent years there has been a systematic effort to generate laboratory
flows which satisfy Eq. (13) over relatively large distances (Wiskind, 1962;
Rose, 1966; Champagne et a/., 1970). It is hoped that these experiments will
gradually be generalized to include small amounts of mean gradient
variation.
It is, of course, much easier to postulate a homogeneous turbulent transport situation (e.g., Corrsin, 1952; Reis, 1952; Burgers and Mitchner,
1953a,b; Craya, 1958; Deissler, 1961; Fox, 1964; Courseau and Loiseau,
1972a.b) than to generate it in the laboratory.
We can supplement the meanfield homogeneity condition which relates to
condition (a) above with a look at the meanfield time stationarity condition,
which is a kind of time scale limitation, condition (b). With momentum
transport time scale T, already estimated for a turbulent boundary layer, we
can ask whether the mean velocity gradient changes appreciably in this time
interval, observing in the convected frame. The analog of Eq. (20) is
(63)
l%a I ( T l 4 6 1 Or I W L 1 (T,/2) 4 1
in the convected frame. Estimating just the first of these from the
Blackwelder/Kovasznay data, we find 0.005 and 0.009 at : / a = 0.20 and
0.45, respectively. Condition (63) is well satisfied.
The third and fourth conditions [(c) and (d)] listed at the start of this
scction specify hornogencity of the length and velocity which characterize
the transport mechanism itself. We look at the boundary layer data for T,
and w' variations between zlb; = 0.20 and 0.45; from the data of Kovasznay
P/ ( I / . (1970). and of Blackwelder and Kovasznay and of Klebanoff, we can
cstiniate Table I.