Geoscience Reference
In-Depth Information
summarizes the resulting set of equations used to describe the movement and
evolution of mean flow in the atmosphere.
Important points in this chapter
Derivation methodology
turbulent flow equations are all derived by express-
ing variables as turbulent fluctuations superimposed on mean values and
then using Reynolds averaging rules to remove terms with zero time-average
value.
:
●
Simplifying assumptions
:
often used in the ABL are:
●
T
T
-
in the ideal gas law;
- density fluctuations can be estimated from
(/)(/)
a
r
′
′ <
r
a
v
a
v
r
;
r
′
≈′
q
q
a
1 in the
Boussinesq approximation
;
- subsidence can often be neglected (i.e.,
—
≈ 0) because |
—
|
+′
r
-
(1
r
)
=
a
a
<<
|
w
'|
Geostrophic wind
because the free atmosphere above the ABL is in a steady
state, time differentials in equations describing
u
and
v
are zero and the wind
components are
U
g
:
●
P
/
y
) and
V
g
=
−
(2
r
a
w
.sin(
q
) )
−1
(
∂
∂
=
(2
r
a
w
.sin(
q
) )
−1
(
∂
P
/
∂
x
).
Divergence equation
the continuity equation in the ABL holds for both the
mean and fluctuating components of kinematic velocity, i.e.,
∇=
:
●
.
u
0
and
∇′=
.
u
.
Turbulent flux divergence
in all equations describing mean atmospheric
flow in a turbulent field the divergence of fluxes transferred by turbulent
flow must be included in addition to the divergence of fluxes transferred by
molecular flow.
:
●
Prognostic equations
prognostic equations for mean atmospheric flow are
all similar to those for instantaneous atmospheric flow, but they include extra
terms describing turbulent flux divergence (Tables 17.1, 17.2, 17.3, and 17.4).
:
●
Neglecting molecular flow
turbulent transfer is about a million times more
efficient than molecular transfer in the ABL, so it is acceptable to neglect the
divergence of molecular transfer fluxes in prognostic equations for mean flow.
:
●
