Surface Fluxes of Momentum, Heat, and Water Vapor
63
with height. This ratio is represented by the stability parameter, -z/ L, where z is the height
above the surface and L is the Monin-Obukhov length
(3.1 )
where the friction (shear) velocity is u., the fluctuating vertical velocity is w, the mean potential
air temperature is 0 and its fluctuating component is B, the dimensionless parameter k is von
Karman's constant (~ 0.4) and 9 is gravitational acceleration. The three classifications of
atmospheric stability can be expressed in terms of the stability parameter as
unstable stratification - I > 0
neutral
z
0
L '*
(3.2)
stable
z
0
L
<
Monin-Obukhov Scaling
Prandtl set out the concept of the logarithmic wind velocity profile, based on dimensional
analysis. In plane parallel flow, an increase of the horizontal mean velocity in the z direction
is evidence of a downward momentum flux. Thus the gradient of mean velocity is determined
by the shear stress at the earth surface, and the distance from that surface, such that
dV
dz
u.
kz
Upon integration from Zj to Z2 we obtain the familiar log law
V2 - Vj = u. In (~)
k
Zj
where Vj and V2 are the mean longitudinal velocities at elevations Zj and Z2.
(3.3)
(3.4 )
The similarity theory of Monin and Obukhov extended Prandtl's scaling to scalars and into
the unstable and stable regimes. This was accomplished by noting the analogy between scalars
and velocity and by admitting additional variables to the dimensional analysis to account for
the effect of density stratification (i.e. (3.1)). Monin-Obukhov (MO) scaling of mean profiles
in the ASL, for example, yields
dV
u.
dz
kz m L
d0
0·
dz
kz
L
r1q
~
dz
kz q L
with 0.( = -H / pCpu.) being a temperature scale, q.( = -E / pu.) a humidity scale, and
1988, and Kader and Yaglom, 1990). This model represents the lowest sublayer of the ASL
63
with height. This ratio is represented by the stability parameter, -z/ L, where z is the height
above the surface and L is the Monin-Obukhov length
(3.1 )
where the friction (shear) velocity is u., the fluctuating vertical velocity is w, the mean potential
air temperature is 0 and its fluctuating component is B, the dimensionless parameter k is von
Karman's constant (~ 0.4) and 9 is gravitational acceleration. The three classifications of
atmospheric stability can be expressed in terms of the stability parameter as
unstable stratification - I > 0
neutral
z
0
L '*
(3.2)
stable
z
0
L
<
Monin-Obukhov Scaling
Prandtl set out the concept of the logarithmic wind velocity profile, based on dimensional
analysis. In plane parallel flow, an increase of the horizontal mean velocity in the z direction
is evidence of a downward momentum flux. Thus the gradient of mean velocity is determined
by the shear stress at the earth surface, and the distance from that surface, such that
dV
dz
u.
kz
Upon integration from Zj to Z2 we obtain the familiar log law
V2 - Vj = u. In (~)
k
Zj
where Vj and V2 are the mean longitudinal velocities at elevations Zj and Z2.
(3.3)
(3.4 )
The similarity theory of Monin and Obukhov extended Prandtl's scaling to scalars and into
the unstable and stable regimes. This was accomplished by noting the analogy between scalars
and velocity and by admitting additional variables to the dimensional analysis to account for
the effect of density stratification (i.e. (3.1)). Monin-Obukhov (MO) scaling of mean profiles
in the ASL, for example, yields
dV
u.
dz
kz m L
d0
0·
dz
kz
L
r1q
~
dz
kz q L
with 0.( = -H / pCpu.) being a temperature scale, q.( = -E / pu.) a humidity scale, and
1988, and Kader and Yaglom, 1990). This model represents the lowest sublayer of the ASL