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Vorticity in the atmosphere is created in three different ways, which are named in their resultant vorticity. These are; Coriolis vorticity, curvature vorticity, and shear vorticity. For example, at the base of a trough, there is curvature and shear vorticity. Curvature vorticity is due to the increasing cyclonic turning as an air parcel enters ...
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 ...
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.
Shortwave trough with associated vorticity. A shortwave or shortwave trough is an embedded kink in the trough / ridge pattern. Its length scale is much smaller than that of and is embedded within longwaves, which are responsible for the largest scale (synoptic scale) weather systems.
where is the relative vorticity, is the layer depth, and is the Coriolis parameter. The conserved quantity, in parentheses 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
In general, the evolution of vorticity can be broken into contributions from advection (as vortex tubes move with the flow), stretching and twisting (as vortex tubes are pulled or twisted by the flow) and baroclinic vorticity generation, which occurs whenever there is a density gradient along surfaces of constant pressure.
In meteorology, [2] helicity corresponds to the transfer of vorticity from the environment to an air parcel in convective motion. Here the definition of helicity is simplified to only use the horizontal component of wind and vorticity, and to only integrate in the vertical direction, replacing the volume integral with a one-dimensional definite integral or line integral:
In words, this equation says that as a vertical column of water is squashed, it moves toward the Equator; as it is stretched, it moves toward the pole. Assuming, as did Sverdrup, that there is a level below which motion ceases, the vorticity equation can be integrated from this level to the base of the Ekman surface layer to obtain: