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The relative vorticity is the vorticity relative to the Earth induced by the air velocity field. This air velocity field is often modeled as a two-dimensional flow parallel to the ground, so that the relative vorticity vector is generally scalar rotation quantity perpendicular to the ground.
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.
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:
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.
Formula for vorticity can give another explanation of the Stokes' Paradox. The functions (), > belong to the kernel of and generate the stationary solutions of the vorticity equation with Robin-type boundary condition. From the arguments above any Stokes' vorticity flow with no-slip boundary condition must be orthogonal to the obtained ...
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
Circulation can be related to curl of a vector field V and, more specifically, to vorticity if the field is a fluid velocity field, =.. By Stokes' theorem, the flux of curl or vorticity vectors through a surface S is equal to the circulation around its perimeter, [4] = = =