7
4.
'I'urhulcnt atmospheric diffusion is due to the turbulent fluctuations of the
wind velocity: but the fluctuations can be defined only if one knows the
mcan motion. thus the whole theoretical frame depends on knowledge of
the meiiil inotioii.
As a first approximation, in the lower layer of the atmosphere over a flat
country, one has made the following hypotheses:
(a) The mean motion is horizontal and depends only on the altitude
above the ground:
u = u('-),
I) = lj(z).
w = 0
(b) Thc density of the air is constant all over the layer:
p = 1) = const
(this is ;I vcry crude assumption, neglecting the temperature fluctuations and
assuming that the thickness of the layer is very small).
(c) The Reynolds stresses depend only on z.
Thus the Reynolds equations reduce to
wlicrc is ihc iiiigular velocity of the Earth's rotation and cp the latitude. In
tilost ol' thc studics one still ovcrsimplifies, neglecting the Earth's rotation
illid h c horiiontal pressure gradient: thus the rotation of the mean wind
vclocity (Eckirlilnti spiral) disappears and one can take F = 0 (the mean
mot ion is purnllel to the Y axis at any altitude z ) ; then from the simplified
Reynolds equations one deduces
nu
d Z
p
i
- pu'w' = const = T~
. .
- , 2 -
(4.3)
p + pgz + pw - const = pb (mean pressure on the ground)
4.
'I'urhulcnt atmospheric diffusion is due to the turbulent fluctuations of the
wind velocity: but the fluctuations can be defined only if one knows the
mcan motion. thus the whole theoretical frame depends on knowledge of
the meiiil inotioii.
As a first approximation, in the lower layer of the atmosphere over a flat
country, one has made the following hypotheses:
(a) The mean motion is horizontal and depends only on the altitude
above the ground:
u = u('-),
I) = lj(z).
w = 0
(b) Thc density of the air is constant all over the layer:
p = 1) = const
(this is ;I vcry crude assumption, neglecting the temperature fluctuations and
assuming that the thickness of the layer is very small).
(c) The Reynolds stresses depend only on z.
Thus the Reynolds equations reduce to
wlicrc is ihc iiiigular velocity of the Earth's rotation and cp the latitude. In
tilost ol' thc studics one still ovcrsimplifies, neglecting the Earth's rotation
illid h c horiiontal pressure gradient: thus the rotation of the mean wind
vclocity (Eckirlilnti spiral) disappears and one can take F = 0 (the mean
mot ion is purnllel to the Y axis at any altitude z ) ; then from the simplified
Reynolds equations one deduces
nu
d Z
p
i
- pu'w' = const = T~
. .
- , 2 -
(4.3)
p + pgz + pw - const = pb (mean pressure on the ground)