Barotropic

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Barotropic Baroclinic Instability

• Mark Guishard
• April 26, 2004
• Meteo 422

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Barotropic InstabilityNecessary 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
Westerlies
Minimum in PV (q)
Easterlies
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Barotropic Instability
y


-
-
Minimum 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
y (? latitude)
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.
-

-

x (? longitude)
Northern and southern anomalies amplify each
other (note the dashed arrows).
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Example Interaction of TC and ITCZ
From Ferreira, R.N., Schubert, W.H., 1997
Barotropic Aspects of ITCZ Breakdown. Journal of
the Atmospheric Sciences Vol. 54, No. 2, pp.
261285.
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Barotropic Instability
y
Easterlies
Maximum in PV (q)
Weak or no flow
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Barotropic Instability
y
-
-


Maximum in PV (q)


-
-
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Example Breakdown of ITCZ
From Ferreira, R.N., Schubert, W.H., 1997
Barotropic Aspects of ITCZ Breakdown. Journal of
the Atmospheric Sciences Vol. 54, No. 2, pp.
261285.
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Baroclinic InstabilityNecessary conditions

• 1) The vertical shear must have the opposite
  slant to that between adjacent PV anomalies
• 2) The PV gradient (?q/?y) must have an opposite
  sign in each level
• 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. This PV perspective is
  similar to that of barotropic instability, only
  in 3 dimensions rather than 2.

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Baroclinic Instability
Upper Westerlies
z
ve PV
-ve PV
-ve PV
ve PV
Surface Easterlies
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Baroclinic Instability
Upper Westerlies
z


-
-
y
-
-


x
Surface Easterlies
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Baroclinic Instability
Upper Westerlies
z


-
-
y
-
-


x
Surface Easterlies
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Baroclinic instability Phase Locking
z
-

-

y
x
Upper and lower anomalies amplify each other
(note the dashed arrows).
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Baroclinic instability Phase Locking
1) The vertical shear must have the opposite
slant to that between adjacent PV anomalies 2)
The PV gradient (?q/?y) must have an opposite
sign in each level 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. This PV perspective is
similar to that of barotropic instability, only
in 3 dimensions rather than 2.
z
-

-

y
x
Upper and lower anomalies amplify each other
(note the dashed arrows).
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Example
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Reading

• Holton Chapter 8
• pp. 255-262 (The Rayleigh Theorem)
• Understand equations 8.48 - 8.50