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The blue square is
Coriolis forcing due to earth rotation

The purple square is
PGF

The green square is
Gravity

The red square is
Friction
Coriolis force
It acts of the left (right) of the momentum on the Southern (Northern) hemisphere
Gravity force
It points down
PGF
It acts in the direction against the pressure gradient
What is the local rate of change (tendencies) if the sum of all forces is zero?
-u ∇ u (advection of momentum)