The atmospheric surface layer - Turbulence in the Atmosphere - page 221

Figure 10.3 The M-O functions for mean wind shear (left) and mean potential
temperature gradient (right), Eq. (10.12) , from the 1968 Kansas experiment. From
Businger et al .( 1971 ).

The von Kármán constant k was introduced in the early twentieth century to scale
the friction velocity in the fully turbulent region near a wall:

/ρ) 1 / 2
z∂U/∂z

( | τ 0 | u ∗

z∂U/∂z .

≡ =

k (10.13)

The M-O function for mean wind shear, Eq. (10.12) , is defined with k to make
its value in neutral conditions 1.0: φ m ( 0 ) = 1 . 0 . For parallelism φ h and φ c , Eq.

(10.12) , are defined with a k as well.
The Kansas experiments were among the first in which the mean wind and tem-
perature profiles and their turbulent fluxes were measured in the surface layer.
Figure 10.3 shows the resulting M-O plots of φ m and φ h . Each shows a remarkable
collapse of data taken over several weeks and a wide range of stability conditions.
Hogstrom ( 1988 ) proposed that the underlying cause of the substantial variations
in the M-O functions φ m and φ h measured in numerous surface-layer experi-
ments was probe-induced flow distortion (Chapter 16) . He presented results from a
surface-layer experiment in which its effects were removed and other measurement
errors minimized. He suggested the following forms:

4 . 8 L , 7 . 8 L ; stable: φ m = 1 . 0 + φ h = 1 . 0 +

(10.14)

1 − 1 / 4 1 − 1 / 2

19 . 3 z
L

12 z
L

unstable: φ m = − ,φ h = − .