Scaling of Simplified Vorticity Equation at Various Levels of Troposphere

Upper Troposphere

Negligible

 

Zero

 

Middle Troposphere

 

 

Negligible

Zero

Surface

 

Negligible

Zero

 

 

Gray Areas Indicate Terms that Are Large

 

DISCUSSION:          

 

                        Upper Tropospheric Constraints

                       

                        Wind flows through trough and ridge patterns or (V – c) >>> 0 

 

Implications:  Air moves through divergent areas east of trough axes and west of downstream ridge axes.  The divergence decreases the absolute vorticity of these air parcels to such an extent that the vorticity advection term is nearly cancelled. 

 

In the upper troposphere, areas of divergence coincide with areas of cyclonic vorticity advection.

Middle Tropospheric Constraints

 

                        Roughly approximates Level of Non-Divergence

                       

Implications: Absolute Vortticity is conserved.

 

In the middle troposphere, along trajectories (and, in certain restrictive circumstances, streamlines), absolute vorticity is conserved.

Lower Tropospheric Constraints

 

                        Pressure/Height patterns tend to be concentric

                       

Implications: Increases in absolute vorticity (development) are

associated with convergence.