Jökull - 01.12.1972, Page 49

be expressed by an universal function (p (z/L);
the profiles are said to be similar. We can
write the profiles
(17)
d0 dT g Tx / z \
dz dz S K z ^ \ L /
dm mx ( z " \
dz k z ^ \ L j
(9 = potential temperature)
(18)
(19)
Further the Richardson number is given by
A sketch of the form of the function <p (z/L)
was found by Monin and Obukhov (1954) by
using known boundary conditions for the dif-
fusivity coefficients. For neutral conditions
cp (z/L) = 1 , z/L = 0 , whereas KM = k ux z.
For near-neutral conditions or forced convec-
tion near the surface, where the influence of
stability is small we have [ z/L j « 1. For these
conditions Monin and Obukhov expanded cp
as a series around z/L = 0 as
f(t) = ,+^f <21>
where j3 is a numerical constant.
If q)(z/L) is given by (21) and k, /3 and zo
are known then H(1 and Hj can be determined
from (9) and (10) when air temperature and
specific humidity are measured at two heights
zi and and wind speed at one height Z2.
Defining downward fluxes positive we obtain
Hd = K p cp ux
0 (z2) - 0 (zi)
Z9
ln — +
Zl
(22)
H[ = Lv E = k p Lv ux
m (z2) - m (zi)
z2 z2 —
ln _ + /3----------—
zi L
zi
(23)
Further (17) and (21) give
ux
K u (z2)
, z2 „ Z2
ln — + /3 -
zo r L
(24)
when z0«z2. Frorn (15) and (24) together with the log-linear temperature profile we get
ln -
Z2
zj
1 +
T0 u2 (z2)
/3 z2 - Zl
L Z 2
ln —
zi
g 0(z2) - 0(zi) /ln _Z2_j2 ^+/3 22 \2
ln
(25)
Zl
Explicit we have then
L = - A + —■ (l + V 1 + 4B (C -A) )
(26)
JÖKULL 22. ÁR 47