Civil Engineering Reference
In-Depth Information
By expressing these different hypotheses using internal
scales (in particular,
+
ν
=
νν
) we conclude:
t
t
+
+
dU
dU
()
τ
+
==
1
ν
+
y
+
=
κ
y
+
tot
t
+
+
dy
dy
and by integrating this expression, we find a logarithmic
velocity distribution:
1
ln
()
++
+
Uy yB
κ
=
+
[1.25]
The constant
B
does not depend greatly on the Reynolds
number, and varies between
. The von
Kárman constant, within the limit of large Reynolds
numbers, is
and
B
=
4.5
B
=
5.5
, as is also predicted by the
renormalization group theory [TAR 11a, TAR 11b]. The zone
of overlap between the viscous sublayer and logarithmic
sublayer is called the buffer sublayer. It plays a dynamic role
which is crucially important in wall turbulence. The so-called
coherent vortex structures are concentrated mainly in this
zone. The coherent vortices, to which this topic is entirely
dedicated, are responsible for the regeneration of the
Reynolds stresses and the turbulent mixing. A semi-
empirical expression for the velocity distribution, which
corresponds well to the measurements, particularly in the
lower buffer sublayer, is
κ =
0.37
⎛
⎞
+
y
()
++
[1.26]
uy
=
14.5 tanh
⎜
⎝ ⎠
14.5
This expression is based on [RAN 56]
3
, which suggests
(
)
ν
+
=
sinh
2
χ
y
+
t
3 See [HIN 75, p. 622].
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