Geography Reference
In-Depth Information
Fig. 5.1
Correlation between vertical velocity and potential temperature perturbations for upward or
downward parcel displacements when the mean potential temperature θ
0
(z) decreases with
height.
Positive buoyancy production occurs when there is heating at the surface so that
an unstable temperature lapse rate (see Section 2.7.2) develops near the ground
and spontaneous convective overturning can occur. As shown in the schematic of
Fig. 5.1, convective eddies have positively correlated vertical velocity and potential
temperature fluctuations and hence provide a source of turbulent kinetic energy and
positive heat flux. This is the dominant source in a convectively unstable boundary
layer. For a statically stable atmosphere,
BPL
is negative, which tends to reduce
or eliminate turbulence.
For both statically stable and unstable boundary layers, turbulence can be gen-
erated mechanically by dynamical instability due to wind shear. This process is
represented by the mechanical production term in (5.14), which represents a con-
version of energy between mean flow and turbulent fluctuations. This term is
proportional to the shear in the mean flow and has the form
∂
u
∂z
−
¯
∂
v
∂z
¯
u
w
v
w
MP
≡−
(5.15)
MP
is positive when the momentum flux is directed down the gradient of the
mean momentum.
Thus,
if the mean vertical shear near the surface is westerly
(∂
u
∂z > 0), then u
w
< 0 for
MP
> 0.
In a statically stable layer, turbulence can exist only if mechanical production is
large enough to overcome the damping effects of stability and viscous dissipation.
¯
