Ch. 13 Ahrens - Vorticity

• VORTICITY: a measure of SPIN, defined as TWICE the angular rate of rotation of an object about a vertical axis (e.g., ice skater; Figure 13.18).

• EARTH VORTICITY: the spin imparted to the air by the rotating Earth (rotation around a local vertical); is dependent on LATITUDE

• Air parcels do not spin about their local vertical at the Equator (Earth vorticity = "0"); parcels have maximum spin about their vertical axis at the poles. Figure 13.19

• EARTH VORTICITY = 2 x (Rate of Rotation of Earth) x sin (Latitude)

• Rate of Rotation of Earth = 2 x "pie" radians per 24 hours = 7.27 x 10^-5 radians/sec

• In comparison, an old vinyl record album spinning at 33.3 revolutions per minute would translate to roughly: 7 radians/sec

• By convention, Earth Vorticity is defined to be "cyclonic" and is a "+" number

• RELATIVE VORTICITY: the counter-clockwise (CCW) or clockwise (CW) circulation of weather systems. CCW (cyclonic) rotation is considered "+" ... same as Earth; CW (anticyclonic) rotation is considered to be "-"; consists of two parts: relative vorticity due to curved flow and that due to wind shear.

• RELATIVE VORTICITY DUE TO CURVED WIND FLOW: parcels acquire relative vorticity when they encounter curved flow; CCW spin (cyclonically, "+") through the base of a trough; CW spin (anticyclonically, "-") through the crest of a ridge. Figure 13.20

• RELATIVE VORTICTY DUE TO WIND SHEAR: parcels acquire relative vorticity when they encounter horizontal differences in wind speeds; CCW spin (cyclonically, "+") when the wind speeds are greater to the south of the parcel; CW spin (anticyclonically, "-") when the wind speeds are greater to the north of the parcel. (Sometimes referred to as: "shear vorticity.") Figure 13.21

• ABSOLUTE VORTICITY: the sum of EARTH VORTICITY plus RELATIVE VORTICITY

• Absolute Vorticity is almost always a "+" number because Earth Vorticity is usually much greater than negative (anticyclonic ) relative vorticity (i.e., PLANET spin versus PARCEL spin).

• Note: ABSOLUTE VORTICITY is the "vorticity" that is plotted on a 500 mb constant pressure chart; the "vort maxes" are marked with an "X" and the "vort mins" are marked with an "N".

• An increase of absolute vorticity is related to upper-level convergence.

• An decrease of absolute vorticity is related to upper-level divergence.

• Figure 13.23 illustrates how vorticity, vertical air motions and surface storm development are all linked together.

• LEE CYCLOGENESIS: the development of a lee-of-the-mountain trough.

• POTENTIAL VORTICITY (PV) = ABSOLUTE VORTICITY (earth + relative) / DEPTH

• PV is CONSERVED

• As air flows up and over a mountain barrier, it's depth shrinks due to the air being squeezed between the mountain top and the tropopause. Since earth vorticity remains constant, the relative vorticity must decrease to compensate, therefore becoming negative, causing the air to turn anticyclonically.

• As the air descends the lee mountain slope, the column stretches. Once again, if the depth increases, so must the relative vorticity, which must also increase (PV is conserved). This causes the air to now turn cyclonically, thus creating a trough of low pressure known as a "lee-side low."