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MAESTRÍA FORMACIÓN DE FORMADORES DE DOCENTES
Blocking occurs when the flow is directed around the mountain, rather than over it. Smith (1980) constructed an energy argument for blocking, which makes things more intuitive. If the air is able to flow over the obstacle, as is assumed from the lower
boundary condition in section 2.1.1, then, from (2.23), gravity waves will be generated that radiate energy away at a rate:
drag× U ∼ ρUNh20b× U (2.30) and the kinetic energy incident on the mountain would be:
(1 2ρU
2
)h0b× U. (2.31)
Taking the ratio of these two to determine the efficiency, it is shown that the rate of energy loss will exceed the rate of energy supply when Flow = N h0/U > O(1), where
Flow is the low-level Froude number. In other words, when the energy required to scale
the mountain is more than the incoming energy, the flow must avoid the mountain. In this case, the vertical suppression dominates and the fluid parcels are forced to pass around the mountain, while remaining in the horizontal plane. When the low-level Froude number is large enough, so that the incident flow has enough energy, vertical displacement occurs. The depth of the flow that is able to go over the mountain, referred to as the effective height hef f, is determined by the height at which the low-
level Froude number is equal to one:
Flow =
N hef f
U = 1. (2.32)
Below this height, the flow will go around the mountain. The depth over which this occurs is called the blocking depth and is given by:
Zb = h− hef f (2.33)
where h is now the maximum height of the mountain. Figure 2.2 illustrates the sep- aration of the mountain into a blocked layer below and a region of mountain wave generation aloft, where the flow is able to follow the shape of the topography. In re- ality these processes are not so distinct, and the interaction with the orography is far more complex with several other processes occurring simultaneously. Nevertheless, this theory does provide a way of accounting for the low-level orographic drag processes and the suppression of gravity wave generation in certain flow regimes.
Chapter 2. Theoretical considerations
2.1. Theory of orographic drag
drag
× U ∼ ρUNh
20b
× U
(2.30)
and the kinetic energy incident on the mountain would be:
(1
2ρU
2
)h
0
b× U
(2.31)
Taking the ratio of these two to determine the efficiency, it is shown that the rate of
energy loss will exceed the rate of energy supply when F
low= N h
0/U >
O(1), where
F
lowis the low-level Froude number. In other words, when the energy required to scale
the mountain is more than the incoming energy, the flow must avoid the mountain. In
this case, the vertical suppression dominates and the fluid parcels are forced to pass
around the mountain, while remaining in the horizontal plane. When the low-level
Froude number is large enough, so that the incident flow has enough energy, vertical
displacement occurs. The depth of the flow that is able to climb the mountain, referred
to as the effective height h
ef f, is determined by the height at which the low-level Froude
number is equal to one:
F
low=
N h
ef fU
= 1
(2.32)
Below this height, the flow will go around the mountain, the depth over which this
occurs is called the blocking depth and is given by:
Z
b= h
− h
ef f(2.33)
where h is now the total height of the mountain. In reality these processes are not so
discreet and the separation into a region of mountain wave generation aloft and blocked
flow below is far more complex with several other processes occurring simultaneously.
Nevertheless, this theory does provide a way of accounting for the low-level orographic
drag processes and the suppression of gravity wave generation in certain flow regimes.
The expression for the low-level blocking drag is largely independent of the linear
wave theory and is based on empirical experiments and bluff body dynamics. The drag
exerted on the mountain due to blocking at a particular height z is given by (Lott and
Miller, 1997):
D
b(z) = ρC
dl(z)
U(z)|U(z)|
2
(2.34)
2.1. Theory of orographic drag
drag× U ∼ ρUNh
20b× U
(2.30)
and the kinetic energy incident on the mountain would be:
(1
2ρU
2
)h
0
b× U
(2.31)
Taking the ratio of these two to determine the efficiency, it is shown that the rate of
energy loss will exceed the rate of energy supply when F
low= N h
0/U >
O(1), where
Flow
is the low-level Froude number. In other words, when the energy required to scale
the mountain is more than the incoming energy, the flow must avoid the mountain. In
this case, the vertical suppression dominates and the fluid parcels are forced to pass
around the mountain, while remaining in the horizontal plane. When the low-level
Froude number is large enough, so that the incident flow has enough energy, vertical
displacement occurs. The depth of the flow that is able to climb the mountain, referred
to as the effective height h
ef f, is determined by the height at which the low-level Froude
number is equal to one:
Flow
=
N hef f
U
= 1
(2.32)
Below this height, the flow will go around the mountain, the depth over which this
occurs is called the blocking depth and is given by:
Zb
= h− h
ef f(2.33)
where h is now the total height of the mountain. In reality these processes are not so
discreet and the separation into a region of mountain wave generation aloft and blocked
flow below is far more complex with several other processes occurring simultaneously.
Nevertheless, this theory does provide a way of accounting for the low-level orographic
drag processes and the suppression of gravity wave generation in certain flow regimes.
The expression for the low-level blocking drag is largely independent of the linear
wave theory and is based on empirical experiments and bluff body dynamics. The drag
exerted on the mountain due to blocking at a particular height z is given by (Lott and
Miller, 1997):
D
b(z) = ρC
dl(z)
U(z)|U(z)|
2
(2.34)
24
drag
× U ∼ ρUNh20b
× U
(2.30)
and the kinetic energy incident on the mountain would be:
(1
2ρU
2)h
0b
× U
(2.31)
Taking the ratio of these two to determine the efficiency, it is shown that the rate of
energy loss will exceed the rate of energy supply when Flow
= N h0/U >
O(1), where
Flow
is the low-level Froude number. In other words, when the energy required to scale
the mountain is more than the incoming energy, the flow must avoid the mountain. In
this case, the vertical suppression dominates and the fluid parcels are forced to pass
around the mountain, while remaining in the horizontal plane. When the low-level
Froude number is large enough, so that the incident flow has enough energy, vertical
displacement occurs. The depth of the flow that is able to climb the mountain, referred
to as the effective height hef f, is determined by the height at which the low-level Froude
number is equal to one:
Flow
=
N hef f
U
= 1
(2.32)
Below this height, the flow will go around the mountain, the depth over which this
occurs is called the blocking depth and is given by:
Zb
= h
− hef f
(2.33)
where h is now the total height of the mountain. In reality these processes are not so
discreet and the separation into a region of mountain wave generation aloft and blocked
flow below is far more complex with several other processes occurring simultaneously.
Nevertheless, this theory does provide a way of accounting for the low-level orographic
drag processes and the suppression of gravity wave generation in certain flow regimes.
The expression for the low-level blocking drag is largely independent of the linear
wave theory and is based on empirical experiments and bluff body dynamics. The drag
exerted on the mountain due to blocking at a particular height z is given by (Lott and
Miller, 1997):
Db(z) = ρCdl(z)
U(z)|U(z)|
2
(2.34)
24
2.1. Theory of orographic drag
drag
× U ∼ ρUNh
20b
× U
(2.30)
and the kinetic energy incident on the mountain would be:
(1
2ρU
2
)h
0
b× U
(2.31)
Taking the ratio of these two to determine the efficiency, it is shown that the rate of
energy loss will exceed the rate of energy supply when F
low= N h
0/U >
O(1), where
F
lowis the low-level Froude number. In other words, when the energy required to scale
the mountain is more than the incoming energy, the flow must avoid the mountain. In
this case, the vertical suppression dominates and the fluid parcels are forced to pass
around the mountain, while remaining in the horizontal plane. When the low-level
Froude number is large enough, so that the incident flow has enough energy, vertical
displacement occurs. The depth of the flow that is able to climb the mountain, referred
to as the effective height h
ef f, is determined by the height at which the low-level Froude
number is equal to one:
F
low=
N h
ef fU
= 1
(2.32)
Below this height, the flow will go around the mountain, the depth over which this
occurs is called the blocking depth and is given by:
Z
b= h− h
ef f(2.33)
where h is now the total height of the mountain. In reality these processes are not so
discreet and the separation into a region of mountain wave generation aloft and blocked
flow below is far more complex with several other processes occurring simultaneously.
Nevertheless, this theory does provide a way of accounting for the low-level orographic
drag processes and the suppression of gravity wave generation in certain flow regimes.
The expression for the low-level blocking drag is largely independent of the linear
wave theory and is based on empirical experiments and bluff body dynamics. The drag
exerted on the mountain due to blocking at a particular height z is given by (Lott and
Miller, 1997):
D
b(z) = ρC
dl(z)
U(z)|U(z)|
2
(2.34)
24
Figure 2.2: Illustration of effective height (hef f) and blocking depth (Zb) of an idealised
mountain with incoming wind U .
wave theory and is based on empirical experiments and bluff body dynamics. The drag exerted on the mountain due to blocking at a particular height z is given by (Lott and Miller, 1997):
Db(z) = ρCdl(z)
U (z)|U(z)|
2 (2.34)
where l(z) is the width of the obstacle in the direction of the flow and Cd is the drag
coefficient. The width is defined in such a way that it reduces to zero at the top of the mountain and is given as a fraction of the length along the base of the mountain (2b):
l(z) = 2b ( Zb− z z )1/2 . (2.35)