Geography Reference
In-Depth Information
We can estimate the magnitude of the geopotential fluctuation δ by scaling
the terms in the momentum equation (11.1). For this purpose it is convenient to
compare the magnitude of the horizontal inertial acceleration,
U
2
/L
(
V
·∇
)
V
∼
with each of the other terms in (11.1) as follows:
|
|
|
|
∼
∂
V
/∂t
/
(
V
·∇
)
V
1
(11.5)
w
∗
∂
V
/∂z
∗
|
|
/
|
(
V
·∇
)
V
| ∼
WL/UH
≤
1
(11.6)
Ro
−
1
|
f
k
×
V
|
/
|
(
V
·∇
)
V
| ∼
fL/U
=
≤
1
(11.7)
δ/U
2
|
∇
|
/
|
(
V
·∇
)
V
| ∼
(11.8)
10
−
4
s
−
1
, the
Rossby number Ro is small so that to first approximation the Coriolis force and
pressure gradient force terms balance. In that case, δ
We have shown previously that in middle latitudes where f
∼
∼
fUL
. In the equato-
10
−
5
s
−
1
and the Rossby number is of order unity or
greater. Therefore, it is not appropriate to assume that the Coriolis force balances
the pressure gradient force. In fact, (11.5)-(11.8) show that if the pressure gradi-
ent force is to be balanced in (11.1), the geopotential perturbation must scale as
δ
rial region, however, f
≤
100 m
2
s
−
2
, and geopotential perturbations associated with equato-
rial synoptic-scale disturbances will be an order of magnitude smaller than those
for midlatitude systems of similar scale.
This constraint on the amplitude of geopotential fluctuations in the tropics has
profound consequences for the structure of synoptic-scale tropical motion systems.
These consequences can be understood easily by applying scaling arguments to
the thermodynamic energy equation. It is first necessary to obtain an estimate of
the temperature fluctuations. The hydrostatic approximation (11.2) implies that for
systems whose vertical scale is comparable to the scale height
U
2
∼
∼
(H /R)∂/∂z
∗
∼
U
2
/R
T
=
(δ/R)
∼
∼
0.3 K
(11.9)
Therefore, deep tropical systems are characterized by practically negligible
synoptic-scale temperature fluctuations. Referring to the thermodynamic energy
equation, we find that for such systems
∂
∂t
+
T
0.3Kd
−
1
V
·
∇
∼
In the absence of precipitation the diabatic heating is caused primarily by the
emission of long wave radiation, which tends to cool the troposphere at a rate
