TRANSPORT MODEL I.IMITA'I IONS IN TURBULENCE
51
simplification in the diffusive term of Eq. (79) shows that only the symmetric
part of D influences the transport; a term like m ( ' . Y l i x 3 is multiplied by
If it were experimentally feasible in B prescribed flow field, we could
successively set up r fields whose mean gradients lie along artesian axis
directions. With measurement of i u and Vr in each case, we could determine
the components of D directly.
Johnson's (1957, 1959) experiment on the mean and fluctuating temperature fields during boundary layer heat transfer from a warm wall provides
the data for determination of one relation between D components. The
example is two dimensional in the mean, so we write only xI (streamwise)
and x3 (normal to wall) components. In addition to Eq. (78) for F,,
(80)
F, = - D 3 , df'/c?x, - D3J c?r/3x3.
estimate
P l . 3 + D 3 , ) .
The mean temperature gradient V r is dominantly along -x3, so we
The heat flux vector is
(82)
-
- -0.915
[ 0.40 ]*
F = ; u = lyul
We note in passing that -% is not even approximately parallel to VI', so a
scalar turbulent diffusivity is out of the question.
A tensor diffwivity must satisfy the diredonat condition implied by
Eq. (70); - D . (Vr) must be parallel to F. This inner product gives
Comparing Eq. (83) with (82), we obtain
which is much like Yaglom's estimate [Eq. (75)].
the boundary prevents any corresponding estimate of D J 1 .
( 8 5 )
D,, z U7Tl, and Dj3 8 Z T 3 3
may suffice for the diagonal components. Also, the estimate that
D1 z 4.5D3, is even more appropriate here than in the atmospheric boundary layer, since the numerical values come from a laboratory boundary
layer flow.
(84)
0 1 3 T - 2 . 3 D 3 3 ,
Unfortunately, the orientation of isothermal surfaces so nearly parallel to
Until appropriate Lagrangian data are available, estimates such as
51
simplification in the diffusive term of Eq. (79) shows that only the symmetric
part of D influences the transport; a term like m ( ' . Y l i x 3 is multiplied by
If it were experimentally feasible in B prescribed flow field, we could
successively set up r fields whose mean gradients lie along artesian axis
directions. With measurement of i u and Vr in each case, we could determine
the components of D directly.
Johnson's (1957, 1959) experiment on the mean and fluctuating temperature fields during boundary layer heat transfer from a warm wall provides
the data for determination of one relation between D components. The
example is two dimensional in the mean, so we write only xI (streamwise)
and x3 (normal to wall) components. In addition to Eq. (78) for F,,
(80)
F, = - D 3 , df'/c?x, - D3J c?r/3x3.
estimate
P l . 3 + D 3 , ) .
The mean temperature gradient V r is dominantly along -x3, so we
The heat flux vector is
(82)
-
- -0.915
[ 0.40 ]*
F = ; u = lyul
We note in passing that -% is not even approximately parallel to VI', so a
scalar turbulent diffusivity is out of the question.
A tensor diffwivity must satisfy the diredonat condition implied by
Eq. (70); - D . (Vr) must be parallel to F. This inner product gives
Comparing Eq. (83) with (82), we obtain
which is much like Yaglom's estimate [Eq. (75)].
the boundary prevents any corresponding estimate of D J 1 .
( 8 5 )
D,, z U7Tl, and Dj3 8 Z T 3 3
may suffice for the diagonal components. Also, the estimate that
D1 z 4.5D3, is even more appropriate here than in the atmospheric boundary layer, since the numerical values come from a laboratory boundary
layer flow.
(84)
0 1 3 T - 2 . 3 D 3 3 ,
Unfortunately, the orientation of isothermal surfaces so nearly parallel to
Until appropriate Lagrangian data are available, estimates such as