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Atmospheric Dynamics II > chapter 3 > Flashcards

chapter 3 Flashcards

1
Q

The large scale flow in the atmosphere is nearly

A

geostrophic

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2
Q

the large scale flow in the atmosphere is nearly geostrophic

the ………………. and …………………. are …………………..

A

wind and mass fields are virtually in balance

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3
Q

the large scale flow in the atmosphere is nearly geostrophic

the wind and mass fields are virtually in balance

In such an atmosphere, the isobars are

A

straight and parallel and the density is a function of pressure alone (barotropic)

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4
Q

If geostrophy is assumed, there is

A

no vertical motion and there is no change in the spatial patterns of the height of isobaric surfaces.

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5
Q

If geostrophy is assumed, there is no vertical motion and there is no change in the spatial patterns of the height of isobaric surfaces.

Hence, geostrophy cannot be used to

A

understand the development of weather systems

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6
Q

Hence, geostrophy cannot be used to understand the development of weather systems, which requires

A

time changes in the spatial patterns of the height of isobaric surfaces

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7
Q

………………………………………. can be used to understand the development of weather systems in ……………………………….

A

Quasi-geostrophic theory

a baroclinic atmosphere

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8
Q

In a baroclinic atmosphere, the

A

surfaces of constant pressure and density intersect each other forming solenoids that leads to direct circulation and vertical motion.

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9
Q

In a baroclinic atmosphere, the surfaces of constant pressure and density intersect each other forming solenoids that leads to direct circulation and vertical motion.

In such an atmosphere,

A

the spatial pattern of height field changes with time.

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10
Q

Hence, the slight deviation of geostrophy (quasi-geostrophic) is of great importance to

A

understanding of atmospheric flow and weather systems

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11
Q

The Quasi-Geostrophic (QG) Momentum Equations

For this analysis, it is convenient to use the

A

isobaric coordinate system

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12
Q

For this analysis, it is convenient to use the isobaric coordinate system because

A
  • meteorological measurements are generally referred to constant pressure surfaces and
  • the dynamical equations are somewhat simpler in isobaric coordinates than in height coordinates.
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13
Q

The scalar and vector horizontal momentum equations in (x,y,z) coordinate system can be written as:

A
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14
Q

The scalar and vector horizontal momentum equations in (x,y,z) coordinate system can be written as:

where

A
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15
Q

Equation (1) can be transferred to

A

x,y,p coordinates

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16
Q

Equation (1) can be transferred to (x,y,p) coordinate system as follows:

A
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17
Q

LHS of Eq.(2) can be expanded as follows:

A
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18
Q

The QG Momentum Equations

Consider the momentum equation in vector form (Eq.3)

A
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19
Q

The QG Momentum Equations

after considering the momentum equation in vector form

now you should

A

Split the horizontal wind into geostrophic and ageostrophic components

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20
Q

The QG Momentum Equations

after concidering the momentum equation in vector form

plitting the horizontal wind into geostrophic and ageostrophic components:

A
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21
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:

the next step is

A

Substituting (4) in the coriolis term in (3)

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22
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:

Substituting (4) in the coriolis term in (3):

A
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23
Q

Midlatitude ß-plane approximation

A

To retain the dynamical effect of the variation of the Coriolis parameter with latitude, f can be approximated by expanding its latitudinal dependence in a Taylor series about a reference latitude O| o

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24
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:
  • Substituting (4) in the coriolis term in (3):

The next step is

A

Now, we replace the Coriolis parameter by f= f0 +ßy , so that the momentum equations (Eq.5) become:

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25
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:
  • Substituting (4) in the coriolis term in (3):
  • Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become:

the next step is

A

Expanding the RHS of Eq.(6)

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26
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:
  • Substituting (4) in the coriolis term in (3):
  • Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become:
  • Expanding the RHS of Eq.(6)

the next step is

A

The last term in (7) is very small, and can be ignored, so we now have:

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27
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:
  • Substituting (4) in the coriolis term in (3):
  • Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become:
  • Expanding the RHS of Eq.(6)
  • The last term in (7) is very small, and can be ignored, so we now have

but the next step is

A

By the definition of the geostrophic wind

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28
Q

The QG Momentum Equations

  • Consider the momentum equation in vector form (Eq.3):
  • Splitting the horizontal wind into geostrophic and ageostrophic components:
  • Substituting (4) in the coriolis term in (3):
  • Now, we replace the Coriolis parameter by f = f0 + ßy , so that the momentum equations (Eq.5) become:
  • Expanding the RHS of Eq.(6)
  • The last term in (7) is very small, and can be ignored, so we now have
  • By the definition of the geostrophic wind

the next step is

A

Substituting (9) in (8), the first two terms on the right-hand side of (8) cancel, resulting in

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29
Q

The approximate QG horizontal momentum equation thus has the form:

A
30
Q

The rate of change of momentum following the total motion is approximately equal to

A

the rate of change of the geostrophic momentum following the geostrophic wind

31
Q

The rate of change of momentum following the total motion is approximately equal to the rate of change of the geostrophic momentum following the geostrophic wind:

A
32
Q

……………………………………………………………………… is approximately equal to the rate of change of the geostrophic momentum following the geostrophic wind

A

The rate of change of momentum following the total motion

33
Q

As discussed earlier, though the atmosphere is close to being in geostrophic balance, the unbalanced component of the wind (the ageostrophic wind) is very important for

A

the dynamics of synoptic disturbances

34
Q

Now, we derive an equation for the ageostrophic wind. For this, consider the

A

simplified horizontal momentum equations

35
Q

Now, we derive an equation for the ageostrophic wind. For this, consider the simplified horizontal momentum equations:

A
36
Q

Thus, the ageostrophic wind, which is the

A

deviation of the real wind from the geostrophic wind,

37
Q

Thus, the ageostrophic wind, which is the deviation of the real wind from the geostrophic wind, is mathematically expressed as:

A
38
Q

The ageostrophic wind is a measure of the

A

horizontal acceleration

39
Q

As shown in figure, the ageostrophic wind points to the

A

left of the geostrophic acceleration (in NHS)

40
Q

the ageostrophic wind figure

A
41
Q

the bold line is representing

A

the height contour

42
Q

the thin line represents

A

isotachs

43
Q

the wind barbs represent

A

the geostrophic wind

44
Q

the figure represents

A

a typical jet streak

45
Q

ageostrophic wind is to the left of the geostrophic acceleration, the ageostrophic wind will be oriented as

A
46
Q

the ageostrophic wind is divergent in

A

the right entrance and left-exit regions of the jet streak

47
Q

the ageostrophic wind is convergent in

A

the other regions

48
Q

the ageostrophic wind is divergent in the right entrance and left-exit regions of the jet streak, and convergent in the other regions

This leads to

A

upward motion in the right-entrance and left-exit regions and downward motion in the other two regions of the jet streak.

49
Q

The Isallobaric Wind – Vector Form

step 1

A

Expanding the total derivative on the RHS of Eq.12:

50
Q

Thus the forcing of the ageostrophic wind can be divided conveniently into the two parts, the

A

isallobaric wind and the advective wind.

51
Q

the isallobaric wind is writen as

A
52
Q

The scalar components of the isallobaric wind can be obtained as:

A
53
Q

from the equation of isallobaric wind

is determined by the

A

gradient of the isolines of do p/do t

54
Q

what are the isolines

A

These are the lines connecting the equal amounts of surface pressure change (isallobars)

55
Q

These are the lines connecting the equal amounts of surface pressure change (isallobars). In figure, we have:

A
56
Q

The direction of the isallobaric wind is

A

perpendicular to the isallobars

57
Q

The direction of the isallobaric wind is perpendicular to the isallobars, always pointing

A

towards the falling pressure

58
Q

The direction of the isallobaric wind is perpendicular to the isallobars, always pointing towards the falling pressure (i.e., pointing to

A

the minimum value where the strongest pressure decrease) in surface pressure is located.

59
Q

the second term on the RHS of is the

A

advective term

60
Q

The scalar components of the advective wind can be written as:

A
61
Q

The advective wind arises when

A

the geostrophic wind is not uniform, as in diffluent or confluent flow pattern.

62
Q

In diffluent flow pattern (fig), the geostrophic wind

A

decreases in positive x-direction

63
Q

In diffluent flow pattern (fig), the geostrophic wind decreases in positive x-direction due to

A

the larger spacing between the isobars indicating smaller pressure gradient.

64
Q

In the analogous case of a confluent flow the wind speed will

A

increase

65
Q

The divergence of the isallobaric wind is:

A
66
Q

Divergence of the isallobaric wind

When heights are falling:

the isallobaric wind is ……………………..

A

convergent

67
Q

Divergence of the isallobaric wind

When heights are rising:

the isallobaric wind is ……………………….

A

divergent

68
Q

The divergence of the advective wind can be obtained as:

where عg is the ………………………….. and Vg.-/عg is the …………………………….

A

where عg is the geostrophic vorticity and Vg.-/عg is the vorticity advection

69
Q

When there is Positive Vorticity Advection (PVA):

the advective wind is ………………

A

divergent

70
Q

When there is Negative Vorticity Advection (NVA):

the advective wind is ……………………..

A

convergent

Atmospheric Dynamics II (9 decks)

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