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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 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:
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
Positive vorticity advection, or PVA, is the result of more cyclonic values of vorticity advecting into lower values of vorticity. It is more generally referred to as "Cyclonic Vorticity Advection" (CVA). In the Northern Hemisphere this is positive, whilst in the Southern Hemisphere it is negative.
Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center. The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the right-hand rule ) while its length ...
A radially symmetrical flow field directed outwards from a common point is called a source flow. The central common point is the line source described above. Fluid is supplied at a constant rate from the source.
The quasi-geostrophic vorticity equation can be obtained from the and components of the quasi-geostrophic momentum equation which can then be derived from the horizontal momentum equation D V D t + f k ^ × V = − ∇ Φ {\displaystyle {D\mathbf {V} \over Dt}+f{\hat {\mathbf {k} }}\times \mathbf {V} =-\nabla \Phi } (3)
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] = = =