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The absolute vorticity is computed from the air velocity relative to an inertial frame, and therefore includes a term due to the Earth's rotation, the Coriolis parameter. The potential vorticity is absolute vorticity divided by the vertical spacing between levels of constant (potential) temperature (or entropy ).
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
The three terms of equation (17) are, from left to right, the geostrophic relative vorticity, the planetary vorticity and the stretching vorticity. Implications [ edit ]
The absolute vorticity is the relative vorticity plus the planetary vorticity: = +. The relative vorticity, ζ {\displaystyle \zeta } , is the rotation of the fluid with respect to the Earth. The planetary vorticity (also called Coriolis frequency ), f {\displaystyle f} , is the vorticity of a parcel induced by the rotation of the Earth.
where is the relative vorticity, is the layer depth, and is the Coriolis parameter. The conserved quantity, in parenthesis in equation (3), was later named the shallow water potential vorticity. For an atmosphere with multiple layers, with each layer having constant potential temperature, the above equation takes the form
Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. As we get closer to the sink, area of flow decreases. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source. As with source flow, the velocity at all ...
The change in the Coriolis parameter and relative vorticity work against each other, creating a wave-like phenomenon. When looking at zonal flow from east to west, this effect is not occurring. This is because the change in the Coriolis parameter and the change in relative vorticity work in the same direction.
Crocco's theorem is an aerodynamic theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first enunciated by Alexander Friedmann for the particular case of a perfect gas and published in 1922: [1]