Jökull - 01.12.1972, Side 50

where A =
ln
, C =
/3 Z2
Z2 ’
ln —
zo
6 (Z2) - 9 (zi)
U2 (z2)
zo I
z2
In —
zi
/3 (Z2 - Zl)
Z2
ln —
zi
If the air temperature ancl the wind velocity
are only measured in the height of z2 and the
air temperature is assumed to be known at the
height zi = zo a simpler expression is founcl for
the Monin and Obukhov length
L = _A + -i (27)
VALIDITY OF THE THEORY
ON THE PRESENT GLACIER.
DISCUSSION
The theory above is worked out under the
assumption I z/L | « 1. On a melting glacier
the air is usually stable and some limit must
be chosen for application of the theory. Prefer-
ably this limit should be chosen both in view
of the validity of the assumption (16) and of
eq. (21). According to Högström (1967) evidence
supports the assumption tliat Kw = KH for all
stabilities. Experience shows further that the
assumption (16) is plausible for near-neutral
stabilities ancl forced convection near the sur-
face of the earth. For increasing stability the
turbulence abates and momentum is transport-
ed more easily by the wave like motion than
heat is. Kn decreases therefore more rapidly
than KM with increasing stability. Numerical
values for the variation of the ratio KH/KM
with stability have been given by many authors
(Lumley and Panofsky 1964). In the present
study this effect was ignored and tlie theory
described above applied for Ri < 0.10. This
value corresponds to tliat found by McVehil
(1964) as a validity-limit for the log-linear wind
profile.
With stronger stability than corresponding to
Ri between 0.1 and 0.2 the turbulence in the
surface layer is damped out so much that radia-
tion divergences, molecular processes and gravi-
ty waves become so important that the assump-
tions of the similarity theory fail. No theory
seems to exist for calculation of the flux-density
of enthalpy for these extreme stabilities.
There has been a frequent discussion on the
value of /3 (Lumley and Panofsky 1964). Using
Monin and Obukhov’s data for J z/L | « 1,
R. J. Taylor (1960) found /3 = 6. For stable
conditions McVehil (1964) found fj = 7. In tlie
present paper (3 — 6 was chosen as a practical
approximation.
The requirements
for observational conditions
In the theory of the Prandtly layer one as.
sumed an aerodynamically rough surface, hori-
zontal homogenity and stationarity. Now we
look at these requirements.
The roughness parameter zo can be very small
for a glacier surface and in light winds a
viscous boundary layer can appear over the
aerodynamically smooth surface. According to
Nikuradses test a surface is said to be aero-
dynamically rough if the Reynolds number
zo ux
---- >2.5 (28)
v
and aerodynamically smooth if
zo ttx
<0.13 (29)
V
For a roughness parameter of zo = 0.1 cm and
molecular viscosity y = 0.15 cm2/s the in-
equality (28) requires friction velocity ux > 3.75
cm/s and (29) that ux < 0.20 cm/s. From the
logarithmic wind profile we find that the in-
equality (28) corresponds to u2 > 90 cm/s, where
u2 is the velocity at the height of 2 m. It will
be seen later that at the present glacier the
current coulcl be considered to be turbulent.
The assumption of constancy with height of
tlie vertical lluxes for momentum and enthalpy
involves strong requirements for steady state
conditions and liorizontal uniformity. In pract-
ice this assumption will never be fulfilled. By
permitting a 4% variation of these fluxes over
2 meters we can get an estimate of correspond-
48 JÖKULL 22. ÁR