1. SO254 – relative and planetary vorticity

2. What is vorticity?
Many meteorological web sites include some form of vorticity contours on the 500-mb charts
Why? How does having contours of vorticity help a meteorologist understand the atmosphere?
Vorticity is a measure of spin, and charts of relative vorticitiy help quickly identify areas with greatest spin (troughs and ridges)
Vorticity advection is directly related to rising and sinking motion
Vertical motions are directly tied to clouds (rising motion  clouds; sinking motion  clear skies)
In the charts at right, the contours show relative vorticity
Yellow and orange (top) and red (bottom) is cyclonic vorticity
Blue (bottom) shows anticyclonic vorticity
Do the areas of cyclonic vorticity tend to show up in troughs, or ridges?

3. What is vorticity? Vorticity is a measure of spin
First, some math:
On a weather chart (like the 500 mb chart), want to measure spin about a vertical axis
Like if you stuck a pencil or a pinwheel on the 500 mb chart, would it spin? And in what way?
So isolate the “vertical vorticity” :
This quantity is also often called “relative vorticity”

4. Relative (vertical) vorticity
Relative (vertical) vorticity is not a measure of “vertical spin”, but rather a measure of horizontal spin
The word “vertical” comes from the fact that it’s the component of the vorticity vector, and the axis of the spin points in the vertical direction
Advantage of relative vorticity: in one variable, both u and v wind components are used
Example: calculate the relative vorticity for these two cases:
50 nm
50 nm
50 nm
50 nm

5. More on relative vorticity,
Measure of local spin
Sign convention:
Positive spin, or positive vorticity, is in the same sense as the counter-clockwise rotation of the Earth (the earth would spin counter-clockwise if you looked down on it from above the north pole)
Negative vorticity: clockwise spin
Two types of vorticity: curvature and shear
The calculation of is the same for both curvature and shear
North
East
Positive vorticity
Negative vorticity
These signs (+ / -) of the vorticity will not change between hemispheres. But, the type (cyclonic / anticyclonic) does change: in the N. Hem., cyclonic vorticity is positive. In the S. Hem., cyclonic vorticity is negative.

6. Planetary vorticity: spin arising from rotation of the Earth
The Earth is a rotating sphere.
It imparts vorticity to fluid parcels
Earth vorticity along the vertical axis is called Coriolis: , where f is Coriolis, Ω is the angular speed of earth’s rotation, and θ is latitude
In Southern Hemisphere, Earth’s vorticity is negative (why?)
Adapted from

7. Absolute vorticity: sum of relative and planetary vorticity
To examine the actual spin of an air parcel, need to look at vorticity contributions from both the Earth and the parcels themselves:
Absolute vorticity:
Above the surface, where friction is small, air flow is nearly geostrophic
Can re-name relative vorticity as “geostrophic relative vorticity”
Also can re-name absolute vorticity as “geostrophic absolute vorticity”

8. Importance of vorticity
We will see later that the horizontal advection of vorticity, combined with horizontal divergence and convergence, has major implications for the development of surface pressure systems, of fronts, of precipitation features
We will learn more about advection in the next lesson
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