1. Vorticity
Vertical component of vorticity: i.e., the rotation about the local vertical
There are three types of vorticity used in geophysical fluid dynamics
If the wind is geostrophic, the geostrophic relative vorticity is given by

2. Vorticity y + + x

3. Divergence Divergence: From the continuity equation -
For incompressible flow:
Most meteorologists simply use divergence when they mean the horizontal divergence

4. Divergence

5. Vorticity and Divergence
Why they are important?
What’s the unit?
What’s the order of the magnitude?
Relative Vorticity
(Synoptic Scales)
Why?

6. Vorticity and Divergence (Synoptic Scale)
Relative Vorticity
Same signs for
both terms

7. Vorticity in Nature Coordinates
Curvature effect S n V
Shear effect -
The smaller the R (i.e., curved more, shorter waves), the stronger the curvature term. R is positive for cyclonic circulation and negative for anti-cyclonic circulation.

8. Vorticity ?
curvature
Shear

9. Vorticity Advection L V wind speed Trough Ridge Relative vorticity
Planetary
vorticity
advection

10. Vorticity Advection (shorter Rossby waves)L V
Trough
Ridge
PVA
Postive Vorticity Advection
Wavelength
(PVA)

11. Vorticity Advection (shorter Rossby waves)
PVA
(assume wave solution)
z decreases
with time
ascent
divergence
aloft
convergence
PVA
Adiabatic
cooling

12. Vorticity Advection (shorter Rossby waves)L V
Trough
Ridge
Divergence
PVA

13. Vorticity Advection (shorter Rossby waves)L V
Trough
Ridge
Con.
Div.
NVA
PVA
Waves propagate eastward!

14. Vorticity Advection (shorter Rossby waves)
NVA
(assume wave solution)
z increases
with time
decent
convergence
aloft
divergence
NVA
Adiabatic
warming

15. Vorticity Advection (shorter Rossby waves)
wave speed C
564
570
576
PVA
NVA
Trough
Wave propagation speed
Tropopause z
level of
non-divergence mb
speed U C

16. H L Vertical Coupling PVA NVA Tropopause level of non-divergence
wave speed C
564
570
576
PVA
NVA
Trough z
speed U C
Tropopause
level of
non-divergence mb H L
Will grow
Will grow

17. Low-level cyclone and 500mb heights
5520
5460
direction of
propagation L
warm air mass
cold air mass
warm front
cold front
996
992
988 ** 32 31 .. 39 37 49 46 . 56 52
Upper and low-level coupled together –
upper level trough enhances the low-level cyclone development.

18. Low-level cyclone and 500mb heights
5520
5460
5520
5460 L
upper level trough catches
low-level system – low level
system is decaying.
upper level trough is about to
catch low-level system.