Example Problem:

 

An air parcel at rest with respect to the surface of the earth at the equator in the upper troposphere moves northward to 30N because of the Hadley Cell circulation.  Assuming that absolute angular momentum is conserved, what tangential velocity would the air parcel possess relative to the earth upon reaching 30N? 

 

 

(wr2)a = (Vr)a = [Vr + (Vr)e] = constant   (1)

 

Note that w is positive if rotation is counterclockwise relative to North Pole.  Thus, V is positive if the zonal motion vector is oriented west to east.

 

 [Vr + (Vr)e]f = [Vr + (Vr)e]i                   (2)

 

Solve for Vf, the tangential velocity relative to the earth at the final latitude.

 

Vf =  [Vr + (Vr)e]f – [(Vr)e]f                                          (3)

                  rf

 

 

                  r = radial distance to axis of rotation = R cos        (4)

 

Ve =WRcos                                  (5)

 

Substitute (5) into (3) and simplify by inserting initial Vi = 0

 

Vf = 482.7 km s-1