Atlantic Jet:Stability of jet core

Thermal winds between 930 and 430 hpa

Look at cross sections where the baroclinicity is greatest – those

positions are

Velocity in Cross section-Northern Hemisphere

Temperature in cross section-700hpa

Modern Stability

Modern Stability

LGM Stability

LGM Stability

Mid Atlantic Jet• Look at jet stability at location of greatest barotropic shear at 800 hpa

Mid Atlantic Jet• Also consider vorticity gradient

Find location of max shear and vorticity gradient in LGM

Minnimum vorticity gradient

Maximum Velocity Shear

Cross sections of zonal velocity at location of maximum velocity shear

Mid atlantic modern stability- structure of eddy

Mid atlantic modern stability- Growth by layer

Mid atlantic LGM stability- Structure of Eddy

Mid atlantic LGM stability- Growth by layer

Seeding the mid-atlantic

• Initialize the mid atlantic mean state jet with normal modes from the Western Atlantic

• Look at growth rates instantaneously which can be determined by projection of tendency onto stream function or finite differencing of the standard deviation of perturbation time series (equivalent results)

Seeding the mid-atlanticModern normal mode growth rates areWestern Atlantic = 3.7 * 10 ^ -6Mid Atlantic = 2.6 *10 ^ -6

Seeding the mid-atlanticLGM normal mode growth rates areWestern Atlantic = 5.9 * 10 ^ -6Mid Atlantic = 4.65 *10 ^ -6

2d Atlantic jet -LGM• Define a domain over which the thermal wind between

900 hPa and 400 hPa is above a threshold value.

LGM

2d Atlantic Jet - LGM• Transition between this 2d zonal velocity and the zonal mean zonal

velocity, on a rectangular, singly periodic domain

2d Atlantic Jet - LGM• The jet has horizontal divergence which is nearly compensated for by vertical

divergence• Match is not exact because the conversion from the sphere to the rectangle has a

geometric factor--- IS THERE SOMETHING ELSE HERE?

LOWER LEVEL

2d Atlantic Jet- LGM• The jet has horizontal divergence which is nearly compensated for by vertical

divergence• Match is not exact because the conversion from the sphere to the rectangle has a

geometric factor--- IS THERE SOMETHING ELSE HERE?

UPPER LEVEL

2d Atlantic Jet - LGM• Find the meridional velocity which makes the jet non-divergent and has no flow

through top and bottom boundary• -Doing both is impossible because there is vertical divergence and the conversion

from the sphere to the rectangle has a geometric factor

LOWER LEVEL

2d Atlantic Jet - LGM• Find the meridional velocity which makes the jet non-divergent and has no flow

through top and bottom boundary• -Doing both is impossible because there is vertical divergence and the conversion

from the sphere to the rectangle has a geometric factor

UPPER LEVEL

2d Atlantic Jet - LGM• Eddies after 45 day integration

2d Atlantic Jet - LGM• Eddy growth in upper layer- growth rate 3.5 *10^-6 Smaller than zonally

invariant case

• E fold in 3.3 days

0 0.5 1 1.5 2 2.5 3

x 106

2

4

6

8

10

12

14

layer 1 datalayer 1 fit slope = 3.4849e-006layer 3 datalayer 3 fit slope =3.4958e-006spatial growth == 3.5134e-006+3.537e-006i

2d Atlantic Jet - LGM• Size of eddies by region – left half vs right half and middle half vs edge half

0 0.5 1 1.5 2 2.5 3

x 106

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5Ratio of eddy activity in different parts of the domain as a function of time

time (hours)

ratio

n of

sta

ndar

d de

viat

ions

Layer 1 ratio of left to rightLayer 1ratio of middle to edgeLayer 3 ratio of left to rightLayer 3 ratio of middle to edge

2d Atlantic Jet - LGM• Growth by region – Projection of tendency onto streamfunction

2d Atlantic jet - MODERN• Define a domain over which the thermal wind between

900 hPa and 400 hPa is above a threshold value.

MODERNMODERN

2d Atlantic Jet- MODERN• Transition between this 2d zonal velocity and the zonal mean zonal

velocity, on a rectangular, singly periodic domain

2d Atlantic Jet- MODERN• The jet has horizontal divergence which is nearly compensated for by vertical

divergence• Match is not exact because the conversion from the sphere to the rectangle has a

geometric factor--- IS THERE SOMETHING ELSE HERE?

LOWER LEVEL

2d Atlantic Jet- MODERN• The jet has horizontal divergence which is nearly compensated for by vertical

divergence• Match is not exact because the conversion from the sphere to the rectangle has a

geometric factor--- IS THERE SOMETHING ELSE HERE?

UPPER LEVEL

2d Atlantic Jet - MODERN• Find the meridional velocity which makes the jet non-divergent and has no flow

through top and bottom boundary• -Doing both is impossible because there is vertical divergence and the conversion

from the sphere to the rectangle has a geometric factor

LOWER LEVEL

2d Atlantic Jet- MODERN• Find the meridional velocity which makes the jet non-divergent and has no flow

through top and bottom boundary• -Doing both is impossible because there is vertical divergence and the conversion

from the sphere to the rectangle has a geometric factor

UPPER LEVEL

2d Atlantic Jet-MODERN• Eddies after 25 day integration- vertical tilt = 53 degrees

2d Atlantic Jet - MODERN• Eddy growth in upper layer- growth rate 2.8 *10^-6 Smaller than zonally invariant cases• E fold in 4 days-_-Pulses between upper and lower level- NUMERICAL instability?

0 1 2 3 4 5 6

x 106

0

2

4

6

8

10

12

14

16

18

layer 1 datalayer 1 fit slope = 2.8619e-006layer 3 datalayer 3 fit slope =2.8497e-006spatial growth == 2.3347e-006+2.7205e-006i

2d Atlantic Jet - MODERN• The eddy size and growth by region oscillates in time

Growth rate by region Eddy size by region

0 1 2 3 4 5 6

x 106

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Ratio of eddy activity in different parts of the domain as a function of time

time (hours)

ratio

n of

sta

ndar

d de

viat

ions

Layer 1 ratio of left to rightLayer 1ratio of middle to edgeLayer 3 ratio of left to rightLayer 3 ratio of middle to edge