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In the northern hemisphere, positive vorticity is called cyclonic rotation, and negative vorticity is anticyclonic rotation; the nomenclature is reversed in the Southern Hemisphere. 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 ...
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.
These undulations give the hollows and peaks of altitude. In general, absolute vorticity advection is positive between these two features, but closer to the ridge, whereas it is negative just behind a trough. At the surface, lifting air under positive vorticity advection is reflected by the formation of depressions and troughs.
Any parcel at rest with respect to the surface of the earth must match the spin of the earth underneath it. Looking down on the earth at the north pole, this spin is in a counterclockwise direction, which is defined as positive rotation or vorticity. At the south pole it is in a clockwise direction, corresponding to negative rotation. Thus to ...
This rapid negative acceleration creates a boundary layer which causes a local rotation of fluid at the wall (i.e. vorticity) which is referred to as the wall shear rate. The thickness of this boundary layer is proportional to √ ( v t ) {\displaystyle \surd (vt)} (where v is the free stream fluid velocity and t is time).
Carl Rossby proposed in 1939 [4] that, instead of the full three-dimensional vorticity vector, the local vertical component of the absolute vorticity is the most important component for large-scale atmospheric flow, and that the large-scale structure of a two-dimensional non-divergent barotropic flow can be modeled by assuming that is conserved.
Considering again the case of a subtropical northern hemisphere gyre, the return flow must be northward. In order to move northward (an increase in planetary vorticity ), there must be a source of positive relative vorticity to the system. The relative vorticity in the shallow-water system is: [11]
For sinusoidal or wavelike motions, where Laplacian operators act simply as a negative sign, [4] and the equation's meaning can be expressed with words indicating the sign of the effect: Upward motion is driven by positive vorticity advection increasing with height (or PVA for short), plus warm air advection (or WAA for short). The opposite ...