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⎛
⎝
⎞
⎠
behavior of
uu
+
max
as a function of the Reynolds number
with surprising accuracy. Finally, the passive structures also
affect the wall-normal and spanwise intensities, but to a
lesser extent in comparison to their effect on
uu
+
. Thus, the
maximum wall-normal and spanwise intensities vary with
(
⎜
⎟
)
(
)
+
+
(
)
(
)
and
.
vv
∝
0.2 ln
Re
τ
ww
∝
0.3ln
Re
τ
max
max
4.10 Particle trajectories: Lagrangian approach
4.10.1.
Lagrangian description and transport by
turbulent diffusion
In this topic, we have made the deliberate choice to favor
the Eulerian approach, considering the modifications of a
characteristic at a fixed position in space, over the
Lagrangian approach, which involves analyzing the
variations of a characteristic relating to the fluid particles.
In this section, we briefly touch on the Lagrangian approach
to transport. Readers can consult Chapter 5 of [HIN 75] or
other specialized publications for further details.
()
linked to the fluid particles,
and a homogeneous plane situated at
Consider a characteristic
qt
x
. The fluid particles
transport the quantity
qt
, and contribute to the mean
regeneration of that characteristic in the plane
x
2
by
()
T
1
()
(
)
(
)
[4.41]
∫
vq t
=
q t t v
,
t dt
2
0
0
0
T
2
0
where
v
2
is the Lagrangian velocity component in
direction
x
2
,
t
0
is the time when the particle passes through
the plane
x
2
and
t
is its diffusion time.
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