EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

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EVAT 554OCEAN-ATMOSPHERE DYNAMICS
LECTURE 7

• FILTERING OF EQUATIONS OF MOTION FOR ATMOSPHERE
  (CONT)

(Reference Peixoto Oort, Chapter 3,7)
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Recall from previous lecture
Geostrophic Balance
Geostrophic Wind
Exercise
show
under Boussinesq approximation and assumption
f?constant
Defines a streamfunction
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Winds dont parallel the streamfunction!
under Boussinesq approximation and assumption
f?constant
Defines a streamfunction
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CONVERGENCE AND DIVERGENCE
Northern or Southern Hemisphere?
Winds dont parallel the streamfunction!
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CONVERGENCE AND DIVERGENCE
Northern or Southern Hemisphere?
Quasigeostrophic
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CONVERGENCE AND DIVERGENCE
Northern or Southern Hemisphere?
Near the surface, friction leads to horizontal
convergence
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CONVERGENCE AND DIVERGENCE
Quasigeostrophic
Near the surface, friction leads to horizontal
convergence
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CONVERGENCE AND DIVERGENCE
Relationship between horizontal convergence and
vertical motion
Quasigeostrophic
Near the surface, friction leads to horizontal
convergence
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Vertical Momentum Balance
Length scale L?106m, l?102m Depth scale H?104m,
h ?102m Horizontal velocity scale u,v ?10
ms-1 Vertical velocity scale w ?10-2
ms-1 Horizontal pressure scale ?p ?10 mb 1000
Pa Time Scale L/u ?105s or H/w ?106s
Radius of Earth a6.37x 106m Coriolis parameter
f,f' ?10-4 s-1 Density of Air r ?1 kg
m-3 Horizontal Eddy Viscosity nH ?10-1
m2s-1 Vertical Eddy Viscosity nV ?10-1 m2s-1
10-7 ms-2
10-3 ms-2
10 ms-2
10 ms-2
10-7 ms-2
10-7 ms-2
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Vertical Momentum Balance
Length scale L?106m, l?102m Depth scale H?104m,
h ?102m Horizontal velocity scale u,v ?10
ms-1 Vertical velocity scale w ?10-2
ms-1 Horizontal pressure scale ?p ?10 mb 1000
Pa Time Scale L/u ?105s or H/w ?106s
Radius of Earth a6.37x 106m Coriolis parameter
f,f' ?10-4 s-1 Density of Air r ?1 kg
m-3 Horizontal Eddy Viscosity nH ?10-1
m2s-1 Vertical Eddy Viscosity nV ?10-1 m2s-1
Hydrostatic Balance
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Vertical Momentum Balance
and
Combining these,
rearranging,
Whats the solution?
Scale height
Hypsometric Equation
Hydrostatic Balance
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Vertical Momentum Balance
and
rearranging
Hypsometric Equation
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Vertical Momentum Balance
and
rearranging
Hypsometric Equation
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Vertical Momentum Balance (revisited)
Length scale L?106m, l?102m Depth scale H?104m,
h ?102m Horizontal velocity scale u,v ?10
ms-1 Vertical velocity scale w ?10-2
ms-1 Horizontal pressure scale ?p ?10 mb 1000
Pa Time Scale L/u ?105s or H/w ?106s
Radius of Earth a6.37x 106m Coriolis parameter
f,f' ?10-4 s-1 Density of Air r ?1 kg
m-3 Horizontal Eddy Viscosity nH ?10-1
m2s-1 Vertical Eddy Viscosity nV ?10-1 m2s-1
10-7 ms-2
10-3 ms-2
10 ms-2
10 ms-2
10-7 ms-2
10-7 ms-2
?
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Vertical Momentum Balance (revisited)
Length scale L?106m, l?102m Depth scale H?104m,
h ?102m Horizontal velocity scale u,v ?10
ms-1 Vertical velocity scale w ?10-2
ms-1 Horizontal pressure scale ?p ?10 mb 1000
Pa Time Scale L/u ?105s or H/w ?106s
Radius of Earth a6.37x 106m Coriolis parameter
f,f' ?10-4 s-1 Density of Air r ?1 kg
m-3 Horizontal Eddy Viscosity nH ?10-1
m2s-1 Vertical Eddy Viscosity nV ?10-1 m2s-1
10-7 ms-2
10-3 ms-2
10 ms-2
10 ms-2
10-7 ms-2
10-7 ms-2
?
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Vertical Momentum Balance (revisited)
Consider a parcel displaced displaced from
hydrostatic equilibrium
(1)
(2)
(2)-(1)
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Vertical Momentum Balance (revisited)
Consider a parcel displaced displaced from
hydrostatic equilibrium
Buoyancy Force
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Vertical Momentum Balance (revisited)
Consider a parcel displaced displaced from
hydrostatic equilibrium
Buoyancy Force
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Vertical Momentum Balance (revisited)
Now, consider the Thermodynamics
For an ideal gas we can rewrite this
We consider parcel motion with no diffusion of
heat and no fluxes of heat across the parcel
boundary (Q0)
Adiabatic
or isentropic (since ds/dtQ/T)
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Vertical Momentum Balance (revisited)
Now, consider the Thermodynamics
For an ideal gas we can rewrite this
Potential Temperature
What is useful about this quantity?
q is conserved for adiabatic motion
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Vertical Momentum Balance (revisited)
Now, consider the Thermodynamics
Dry Adiabatic lapse rate
Stability Properties?
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Vertical Momentum Balance (revisited)
Now, consider the Thermodynamics
stable
Thus
neutral
Exercise
unstable
Stability Properties?
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Vertical Momentum Balance (revisited)
stable
neutral
unstable
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Vertical Momentum Balance (revisited)
stable
neutral
unstable