Scaling of Simplified Vorticity Equation at Various Levels of Troposphere

 

 

 

 

 

Upper Troposphere

Negligible

 

 

 

Middle Troposphere

 

 

Zero

 

Surface

 

Negligible

 

 

 

 

 

 



 

 

 

 

 

 

 

 

 

 

Green shading = Terms that are large

 

 

Simplified Barotropic (Natural Coordinates) Vorticity Equation


 

 

Case 1:  Upper Troposphere

 

 

 

 

 

         (1)

 

 

 

 

 

 

 

Horizontal Divergence is “diagnosed” or “associated with” or “coincident” with areas of positive (cyclonic) vorticity advection (and vice versa).  This is because, for example, air parcels streaming from trough axis to ridge axis experience, typically, great horizontal divergence.  This divergence is so great that by the time they reach the ridge axis, their vorticity has been reduced to the value that originally was at the ridge axis. 

 

Please note that  equation (1) does NOT mean that vorticity advection “causes” divergence or that divergence causes vorticity advection.  Equation (1) expresses an association that appears on weather maps.

 

 

Case 2:  Middle Troposphere

 

Horizontal divergence is minimal or zero in the middle troposphere.  Thus,

 

 

 

 

 

 

 

 

 

 

 

 

 

(2a) states that air parcels conserve their absolute vorticity (in the restrictive circumstance of no horizontal divergence).   The is called “Conservation of Absolute Vorticity”.

 

Equation (2b) states that the local changes in vorticity observed at a location would be due simply to the advection of vorticity by the wind.  Essentially the vorticity pattern translates with the trough and ridge pattern responsible for it.

 

 

 

 

 

Created with The GIMP

 

 

 

 

 

Case 3:  Lower Troposphere

 

Since lower tropospheric patterns tend to be nearly concentric circles or ellipses, vorticty advection is minimal or zero (vorticity contours are parallel to height contours or isobars).

 

 

 

 

 

 

 

(3)

 

 

 

Equation (3) states that all the local changes in vorticity will be due to convergence or divergence.   This normally occurs by cross contour flow relative to the closed systems found on, say, sea level weather maps.