Note, the density term is in the pressure gradient force because this is the force per unit mass (so we get rid of ill defined volumes in the atmosphere).


We will deal with vorticity later. For now we keep things farily simple and qualitatively show the net effect of the pressure gradient force and the coriolis fictious force.









The following simple picture might help better visualize this. The horizontal velocity is largest in zone A, then zone B, and finally zone C as the pressure gradient is highest in zone A and lowest in zone C, along the horizontal coordinate x: