EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

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EVAT 554OCEAN-ATMOSPHERE DYNAMICS
LECTURE 6

• FILTERING OF EQUATIONS FOR ATMOSPHERE (CONT)

(Reference Peixoto Oort, Chapter 3)
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Meridional 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
10-4 ms-2
10-3 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic 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
10-4 ms-2
10-3 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic 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
10-4 ms-2
10-3 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2
Rossby Number
Geostrophic Balance Holds when Ro ltlt 1
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic Balance
Geostrophic Wind
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Horizontal Momentum Balance
f 43o
d600 km
W7.27x10-5 s-1
f2Wsin f
Example
5.6 m/s
Geostrophic Wind
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Let us Revisit e.g. the Meridional 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
10-4 ms-2
10-3 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2
What if the acceleration/non-linear term cannot
be neglected?
i.e., Ro ? 1
8
Let us Revisit e.g. the Meridional 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
10-4 ms-2
10-3 ms-2
10-3 ms-2
10-4 ms-2
10-4 ms-2
What if the acceleration/non-linear term cannot
be neglected?
This applies to flows with strong curvature
i.e., Ro ? 1
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Horizontal Momentum Balance
Centripetal acceleration
acV2/R
V(u2v2)1/2
VRw
Gradient Wind Balance
(zonal)
This applies to flows with strong curvature
(meridional)
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Horizontal Momentum Balance
Centripetal acceleration
acV2/R
V(u2v2)1/2
VRw
Gradient Wind Balance
(zonal)
This applies to flows with strong curvature
(meridional)
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Horizontal Momentum Balance
Centripetal acceleration
acV2/R
V(u2v2)1/2
VRw
Gradient Wind Balance
(zonal)
What about flow near the equator?
(meridional)
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Horizontal Momentum Balance
Centripetal acceleration
acV2/R
Near equator (e.g. Hurricane), Coriolis Force is
negligible, and balance is between PGF and
Centripetal acceleration
V(u2v2)1/2
VRw
Cyclostrophic Balance
(zonal)
What about flow near the equator?
(meridional)
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic Balance
Generally an excellent approximation for upper
level winds
Any evidence of breakdown of Geostrophy?
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic Balance
Relationship Between Temperature and Winds?
Advection
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic Balance
Relationship Between Temperature and Winds?
Advection
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Horizontal Momentum Balance
(zonal)
(meridional)
Geostrophic Balance
What can we say about this term?