Gradient Winds

Gradient Wind (or flow) develops only in the absence of friction, when considering curved flow and flows perpendicular to the contours, for the same reason as in geostrophic flow. However, gradient wind is not truly geostrophic because it is constantly moving, thus undergoing an acceleration. Nonetheless, this time, in order for the air to follow parallel to the contours there must consider the effects of the centrifugal force as well as the pressure gradient force and the Coriolis force.

Subgeostrophic Flow is when V < V_g, air curves cyclonically (counter-clockwise), and the CF needs greater than in the geostrophic case in order to balance the PGF.

Supergeostrophic Flow is when V > V_g, air curves anti-cyclonically (clockwise), and the CF does not need to be as great as in the geostrophic case in order to balance the PGF.

Putting it all together…

Geostrophic Wind (and Equations)

Geostrophic Wind is a nonaccelerating flow occurring only in the upper atmosphere (due to the lack of friction) and when the winds are considered at “steady-state” (when the PGF counterbalances the CF). In fact the geostrophic flow is simply a special case of gradient flow that arises when the wind flows parallel to the isobars.

Conservation of Angular Momentum (Derivation of the Coriolis Force)

Angular Momentum takes into account the rotation of the object. Whereas, the conservation of angular momentum is a law of physics that states the angular momentum of a rotating object (with no outside force) remains constant regardless of changes within the system (i.e. Earth’s rotation Ω). This conservation of angular momentum will always be maintained as long as there is no net external torque acting on the object or on the system itself.

Example: Derive the Coriolis Force.

Coriolis Force Motion on a Latitudinal Circle

Coriolis Force—the force per unit mass that results from the rotation of the earth and acts on a moving particle with respect to the earth to deviate it.

•      Perpendicular to the axis of rotation and the velocity vector.
•      Directed to the right (in the Northern Hemisphere) and radially outward from the axis of rotation. 
•      Can only change direction, not magnitude.

Components of the Coriolis force (CF) due to relative motion along a latitude circle. Ra is the apparent radius, Re is the radius of the earth., and omega is Earth's rotational frequency.

Physical Principles: The Coriolis Force

Understanding Weather and Climate (7th Edition) (MasteringMeteorology Series) 7th Edition by Edward Aguado (Author), James E. Burt (Author)