Geography Reference
In-Depth Information
f
¯
u
g
−
∂v
w
∂z
−
−¯
=
u
0
(5.19)
where (2.23) is used to express the pressure gradient force in terms of geostrophic
velocity.
5.3.1
Well-Mixed Boundary Layer
If a convective boundary layer is topped by a stable layer, turbulent mixing can
lead to formation of a well-mixed layer. Such boundary layers occur commonly
over land during the day when surface heating is strong and over oceans when the
air near the sea surface is colder than the surface water temperature. The tropical
oceans typically have boundary layers of this type.
In a well-mixed boundary layer, the wind speed and potential temperature are
nearly independent of height, as shown schematically in Fig. 5.2, and to a first
approximation it is possible to treat the layer as a slab in which the velocity and
potential temperature profiles are constant with height and turbulent fluxes vary
linearly with height. For simplicity, we assume that the turbulence vanishes at the
top of the boundary layer. Observations indicate that the surface momentum flux
can be represented by a
bulk aerodynamic formula
3
u
w
v
w
C
d
V
¯
C
d
V
¯
s
=−
u,
and
s
=−
v
Fig. 5.2
Mean potential temperature, θ
0
, and mean zonal wind, U , profiles in a well-mixed boundary
layer. Adapted from Stull (1988).
3
The turbulent m
ome
ntum flux is often represented in terms of an “eddy stress” by defining, for
example, τ
ex
=
ρ
o
u
w
. We prefer to avoid this terminology to eliminate possible confusion with
molecular friction.
