Tropical Cyclogenesis

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Tropical Cyclogenesis

• Ferreira, R.N., Schubert, W.H., 1997
• Barotropic Aspects of ITCZ Breakdown.
• J. of Atmos. Sci. Vol.54, No.2, pp. 261285.
• Mark Guishard and Young Kwon
• Oct. 4, 2004

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Energy flows for a) baroclinic, b) barotropic
instability.
a)
b)
Barotropic instability Kinetic energy of the
eddies (perturbation KE) grow at the expense of
the mean KE.
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Barotropic Instability Necessary conditions

• 1) The latitudinal shear must have the opposite
  slant to that between adjacent PV anomalies
• 2) The PV gradient (?q/?y) must have an opposite
  sign at each latitude
• 3) The flow must be opposite in direction to the
  phase velocity of the waves.
• Conditions 1) 3) maintain the phase locking
  of the disturbances.

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Barotropic Instability
y
Easterlies
Maximum in PV (q)
Westerlies
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Barotropic Instability
y
Maximum in PV (q)
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Barotropic Instability
y
Upper and lower disturbances must remain locked
in position relative to each other. How?
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Barotropic Instability Phase Locking
y (? latitude)
x (? longitude)
Northern and southern anomalies amplify each
other (note the dashed arrows).
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Barotropic Instability Phase Locking
1) The latitudinal shear must have the opposite
slant to that between adjacent PV anomalies 2)
The PV gradient (?q/?y) must have an opposite
sign at each latitude 3) The flow must be
opposite in direction to the phase velocity of
the waves. Conditions 1) 3) maintain the phase
locking of the disturbances.
y (? latitude)
x (? longitude)
Northern and southern anomalies amplify each
other (note the dashed arrows).
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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Fig. 1
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Fig 1 (cont.)
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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Shallow water equation on Cartesian coordinates
Spherical Coordinate operators
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Convert zonal momentum equation to Spherical
coordinates using the operators
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Equations 1-4
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Derivation of PV equation
Rearrange the Eq. (3) using differentiating by
part
Multiply on both side
of the equation
(I)
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The first term of Eq. (I)
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(II)
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Substitute Eq. (II) into Eq. (I), then
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Mass sink(Q) to parameterize the ITCZ convections
PV equation
The PV source term can be simplified as a
vertical component because the vertical component
of vorticity is dominant (the first term of LHS
will be ). In addition, the
maximum diabatic heating occurs at the mid-level
of convection. As a result, the convection
increases PV in the lower level but decreases in
the upper level. However, the vertical advection
compensate the decrease of PV in the upper level.
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Maximum Latent Heating by convection
PV decrease
Z
vertical velocity
Convection
PV increase
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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Fig. 2
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Eq. (8) and Fig.2

• Express zonally symmetric ITCZ using Eq. (8) and
  the structure of the ITCZ is depicted in Fig. 2
• Questions ?
• Why is planetary vorticity line straight with
  latitude?
• Latitude is not zero where the absolute vorticity
  value is zero.

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Fig 3a
FIG. 3. Breakdown of a 4.58 wide zonally
symmetric vorticity strip centered at 108N with
maximum relative vorticity 3.0 3 1025 s21. The
displayed fields are fluid depth (m), PV (s-1),
and winds (m s -1) at (a) 5 days, (b) 10 days,
and (c) 15 days.
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Fig3b
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Fig 3c
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Barotropically unstable eddy
1m/sec
2m/sec
2m/sec
2m/sec
y
3m/sec
2m/sec
Kinetic energy of mean flow
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Fig.4
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The phase speed of Rossby wave
Around ITCZ, the meridional gradient of PV is
stronger than that of planetary vorticity, so
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Growing Perturbation
Decaying Perturbation
Barotropically unstable eddy
Barotropically stable eddyaxisymmetrization
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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Fig. 5
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Fig. 6
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Fig. 7
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Fig 8a
FIG. 8. Interaction of a cyclone centered at 15
N with ? 2.0 X 10 -4 s-1 and 28 in radius with
a 4.5 wide zonally symmetric PV strip centered
at 10N with ? 3 X 10 -5 s-1. The displayed
fields are fluid depth (m), PV (s-1), and winds
(m s -1) at (a) 2 days, (b) 5 days, and (c) 10
days.
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Fig 8b
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Fig 8c
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Fig. 9
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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Eqns 9 10
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Fig. 10
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Fig 11a
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Fig 11b
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Fig 11c
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Fig. 11d
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Fig. 12
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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Fig. 13
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Fig. 14 a
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Fig. 14b
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Fig. 16
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Outline of Paper

• 1) Introduction
• 2) Shallow Water Equations
• 3) Breakdown of zonally symmetric PV strips
• 4) Interaction between a cyclone and a zonally
  symmetric PV strip
• 5) The breakdown of an ITCZ of limited zonal
  extent
• 6) The breakdown of an irregularly shaped ITCZ
• 7) Concluding Remarks

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