TI: RBI: LEN7 ATMOSPHERIC DIF FUSlOh
9
with with great accuracy; Praiidtl (1932) aid von Krirmitn (1930) gave
theoretical jiistifications of this law based respectively on the (very
controversial) idea of the Mischrtgsweg and on general similarity considerations (which seemed quite plausible). Prandtl's formula reads
(4.6)
Si(2) = 5.75(1o/p)1i* log(xlz/k)
where k is a length characteristic of the roughness of the plate. To this
velocity profile corresponds the linear law for the turbulent velocity
coefficient
(4.7)
y*(z) = 0.174(~0/p)"~~
A considerable amount of experimental research has been devoted to the
verification of the logarithmic law in the lower layer of the atmosphere. One
' of the most complete series of measurement is due to Rossby and Montgomery (1935): they use the formula
. ..
(4.8)
U ( Z ) = 5.75(201p)"~ log[(= -t- Z,,)/Zo]
which has the advantage over (4.6) ofgiving ii(0) = 0. When the temperature
gradient is adiabatic, = lT/lOO m, they found rather good agreement,
taking the values (cm)
zo = 0.2.5
over snow
zo = 0.93
over grass
zo = 4.00
over a calm sea
Paeschke (1937) introduces two constants zo and tb
(4.9)
ii(z) = 5 . 7 5 ( ~ ~ / p ) ' ' '
Iog[(z - zb)/zO]
His measurements, done with a hot-wire anemometer, are the most precise
and were done over a great number of varied grounds. He gives the following values (cm)
z;, = 3
z, , = 0.5
over snow
z; = 20
:,, = 3.2 over short grass
z;, = 30
z,, = 3.9
over high grass
$, = 45 zo = 6.7 over field of beets.
It miist bc pointed out that if z > 1 m, the three formulas (4.6). (4.8), and
(4.9) practically coincide.
We did ourselves a series of measurements during World War 11 (unpublished) in the layer 0 < z < 10 m over the Hamada. a very flat plateau in the
Sahara. The Wamada extends over hundreds of miles, thus the homogeneity
9
with with great accuracy; Praiidtl (1932) aid von Krirmitn (1930) gave
theoretical jiistifications of this law based respectively on the (very
controversial) idea of the Mischrtgsweg and on general similarity considerations (which seemed quite plausible). Prandtl's formula reads
(4.6)
Si(2) = 5.75(1o/p)1i* log(xlz/k)
where k is a length characteristic of the roughness of the plate. To this
velocity profile corresponds the linear law for the turbulent velocity
coefficient
(4.7)
y*(z) = 0.174(~0/p)"~~
A considerable amount of experimental research has been devoted to the
verification of the logarithmic law in the lower layer of the atmosphere. One
' of the most complete series of measurement is due to Rossby and Montgomery (1935): they use the formula
. ..
(4.8)
U ( Z ) = 5.75(201p)"~ log[(= -t- Z,,)/Zo]
which has the advantage over (4.6) ofgiving ii(0) = 0. When the temperature
gradient is adiabatic, = lT/lOO m, they found rather good agreement,
taking the values (cm)
zo = 0.2.5
over snow
zo = 0.93
over grass
zo = 4.00
over a calm sea
Paeschke (1937) introduces two constants zo and tb
(4.9)
ii(z) = 5 . 7 5 ( ~ ~ / p ) ' ' '
Iog[(z - zb)/zO]
His measurements, done with a hot-wire anemometer, are the most precise
and were done over a great number of varied grounds. He gives the following values (cm)
z;, = 3
z, , = 0.5
over snow
z; = 20
:,, = 3.2 over short grass
z;, = 30
z,, = 3.9
over high grass
$, = 45 zo = 6.7 over field of beets.
It miist bc pointed out that if z > 1 m, the three formulas (4.6). (4.8), and
(4.9) practically coincide.
We did ourselves a series of measurements during World War 11 (unpublished) in the layer 0 < z < 10 m over the Hamada. a very flat plateau in the
Sahara. The Wamada extends over hundreds of miles, thus the homogeneity