J. I.. I.IJMI.EY A N D H. KHAJEH-NOCiWI
I
I
1
1. 0
2.0
1 0
4. 0
Y/ L
Fic;. 8. Thc nc\rmalided dissipation. Townscnd's valucs or the ahscissa are clearly incorrcct
siirue they rcsult in ;I displacement orthe peak of the prcductinn. which can he ohtained Without
assumption from the mean vclocitq curve. Thc ithscissa tias heen rcnornializcd so that the peak
of the mearured prixfuction occurs in thc same pla~v its that ohtititid from the mean velocity
prntilc.
Uiifortunatcly. we were not able to use significant values of this term due
to a second order nonlinear computational instability, triggered by the addition of points at the edge of the mesh; even very small values of this
ccxficicnt rcquired drastic decrcascs in the size of the time step. This is not a
fundamental difficulty, however; we must simply find a differencing schemc
for these terms which is more stable. or find a way of adding points to the
mcsh which will not excite the instability.
Thc peak in the curve of? will also be essentially removed by the use of
this term; at present, the flow is too isotropic ncar the center line, and
ooiisequently there is not enough T: production there. Increasing the anisotropy there will make theE production more uniform and permit a reduction
in the overall level of E.
It is worth mentioning that in thc range of vnlues of .u/d in which Townsend's measurements were made (500 lOOO), our values changed only a total
of 4";;, which is itbout the variation observed in Townsend's data; it thus
iippcars perfwily possible that Townsend's measurements are 6- 10 ('.A from
thc true sclf-preserving values (but would appear to be self-preserving). This
is heme out hy the fact that his mcasured Reynolds stress is not self-
I
I
1
1. 0
2.0
1 0
4. 0
Y/ L
Fic;. 8. Thc nc\rmalided dissipation. Townscnd's valucs or the ahscissa are clearly incorrcct
siirue they rcsult in ;I displacement orthe peak of the prcductinn. which can he ohtained Without
assumption from the mean vclocitq curve. Thc ithscissa tias heen rcnornializcd so that the peak
of the mearured prixfuction occurs in thc same pla~v its that ohtititid from the mean velocity
prntilc.
Uiifortunatcly. we were not able to use significant values of this term due
to a second order nonlinear computational instability, triggered by the addition of points at the edge of the mesh; even very small values of this
ccxficicnt rcquired drastic decrcascs in the size of the time step. This is not a
fundamental difficulty, however; we must simply find a differencing schemc
for these terms which is more stable. or find a way of adding points to the
mcsh which will not excite the instability.
Thc peak in the curve of? will also be essentially removed by the use of
this term; at present, the flow is too isotropic ncar the center line, and
ooiisequently there is not enough T: production there. Increasing the anisotropy there will make theE production more uniform and permit a reduction
in the overall level of E.
It is worth mentioning that in thc range of vnlues of .u/d in which Townsend's measurements were made (500 lOOO), our values changed only a total
of 4";;, which is itbout the variation observed in Townsend's data; it thus
iippcars perfwily possible that Townsend's measurements are 6- 10 ('.A from
thc true sclf-preserving values (but would appear to be self-preserving). This
is heme out hy the fact that his mcasured Reynolds stress is not self-