SO441 Synoptic Meteorology
Lesson 6: Potential vorticity
Potential Vorticity
• Concept of potential vorticity:
– Take a column of air defined by two potential temperature surfaces (θ
and θ+Δθ).
– Move this column of air eastward. Force it to go up and over a
mountain range.
– What happens to the column of air??
• It compresses (“fattens”) as it approaches the mountain, and stretches
again on the other side of the mountain
Figure adapted from http://www-das.uwyo.edu/~geerts/cwx/notes/chap12/pot_vort.html
Potential Vorticity
•
Mathematically, what is it?
– Measures absolute vorticity (spin) over the depth of a column of air
PV 
•
f
h
What does it mean that potential vorticity is conserved?
– Following air motion (Lagrangian perspective!!), absolute vorticity divided by depth of
the fluid must remain constant.
D   f 

0
Dt  h 
•
Return to the scenario of easterly flow (a fluid column moves from west to east):
– Along it’s path, potential vorticity must be constant.
– f, Earth’s vorticity, is constant (b/c it moves to the east)
– But h, depth, decreases as it approaches the mountain
• Thus, relative vorticity zeta must also decrease. A ridge forms.
– After passing the mountain, depth increases again
• Thus, relative vorticity zeta must now also increase. A trough forms.
Potential Vorticity
• Physically, potential vorticity is a quantity that
is
– Useful to measure the “spin up” or “spin down” of
an air column for large-scale, adiabatic motion
• The very important conservation property
(that potential vorticity is conserved following
the fluid motion) is valid for
– Atmospheric motions with no friction or diabatic
effects
Potential Vorticity in the real atmosphere
• Here are the average winter 500 mb heights for the NH (left)
and SH (right)
– Note the SH is nearly symmetric about the pole, but the NH is much
more wavy (3 mean troughs, to be exact)
– Why is this the case? What is different about the flow from NH to SH?
Potential Vorticity in the real atmosphere
• Another property of Potential Vorticity is that the
amplification of heights as flow approaches a mountain is
most prnounced in the low levels.
– So 700 mb (left) is much more wavy than 200 mb (right)
Potential Vorticity in the real atmosphere
• The requirement that potential vorticity be conserved is
common in both hemispheres.
– Flow crossing the Andes Mountains (which are VERY tall) results in
ridging over Chile and troughing over Argentina, Uruguay, and Brazil
Figure adapted from http://www-das.uwyo.edu/~geerts/cwx/notes/chap12/pot_vort.html