1. The vector measure of rotation around a point
Vorticity
The vector measure of rotation around a point

2. Mathematical Representation
Vorticity is the curl of the velocity vector
For 3-D vorticity in Cartesian coordinates:
The horizontal relative vorticity is found by
eliminating terms with vertical (w) components:

3. Mathematical Representation
The absolute vorticity (η) is the sum of the relative vorticity (spin of the fluid) and the planetary vorticity (rotation due to the spin of the earth):
Absolute Vorticity
Coriolis Parameter =
2Ωsin(Φ) where
Φ = latitude
Relative Vorticity

4. Mathematical Representation
In natural coordinates, the relative vorticity is:
“Shear Term”
Vorticity due to shear of
the wind
“Curvature Term”
R = Radius of Curvature
Vorticity due to the spin around
a point

5. Divergence
A scalar field (no direction) that measures the tendency of a vector field to spread out

6. Mathematical Representation
In Cartesian coordinates (2-Dimensional):
In natural coordinates:
How the wind speed
changes in the t direction
Note: Convergence
is just
How the wind direction
changes in the n direction

7. Directional Divergence

8. Speed Divergence
Divergence
Convergence

9. The Vorticity Equation
Relates the local rate of change of vorticity to several forcing mechanisms:
Divergence Term
Convergence = Increase
in vorticity
Divergence = Decrease
Tilting Term
Represents effects on vorticity
due to changes in the vertical
velocity (w) in the horizontal
direction
Solenoidal Term
Effects of pressure
gradient force on
changes in vorticity

10. Simplified Vorticity Equation
A scale analysis shows that the tilting and solenoidal terms are much smaller than the other terms
Furthermore, break the total derivative into its local change and advective components to yield:
Divergence term
Advection of absolute vorticity

11. Vorticity Advection Positive Absolute Vorticity Advection (PAVA)
Approaching trough
Rising motion
Surface convergence
Possible intensification of surface low
Negative Absolute Vorticity Advection (NAVA)
Approaching ridge
Sinking motion
Surface divergence
Intensification of anti-cyclones