Vorticity Objectives Define Vorticity Earth f and Relative

Vorticity Objectives • Define Vorticity – Earth ( f ) and Relative vorticity ( ) – Shear and curvature terms in Relative vorticity • Understand how vorticity relates vertical motions in the atmosphere to horizontal convergence and divergence of air. • Identify regions of shear and curvature vorticity and vorticity advection on a weather chart.

Vorticity In large scale meteorology, we usually care most about vorticity along a vertical axis.

Relative Vorticity • The vorticity of moving air relative to the earth’s surface. • The sum of two components: – shear – the change in the wind speed normal to the flow direction – curvature – turning of the air flow • Sign Conventions (NH): – Air that spins CCW has positive relative vorticity – Air that spins CW has negative relative vorticity

Vorticity is the measure of spin of an air parcel

Earth Planetary Vorticity ( f ) Coriolis Force= Velocity * f f = 2 * 7. 292 10‾ 5 /s * sin(latitude) • The earth spins => it has vorticity => all objects on the earth, moving or not, have vorticity due to the earth’s rotation • Earth vorticity is + (-) in the NH (SH) • The magnitude of earth vorticity depends on latitiude – it is maximum + (-) at the N (S) pole, zero at the equator • The coriolis parameter, f, represents the earth vorticity

Absolute Vorticity • Sum of Relative and Earth Planetary vorticity • Absolute vorticity is CONSERVED in adiabatic, frictionless, non-divergent flow (i. e. , columns of air cannot stretch or contract vertically) – Usually applied to barotropic atmosphere • In the NH, earth vorticity (+) is usually always larger than relative vorticity in magnitude => absolute vorticity is positive, but smaller for Clockwise (NH A/CYCL) flow (relative vorticity <0) than Counterclockwise CW (NH CYCL) flow (relative vorticity >0).

Relative Vorticity and Earth Vorticity In this figure, the subscript e (r) indicates Earth (relative) vorticity. DLA Fig. 8. 28

Vorticity Equation 1 4 1. 2. 3. 4. 2 5 3 6 advection of relative ζ creation of ζ through horizontal convergence advection of the Earth’s vorticity creation of ζ by the tilting of vortices rotating about a horizontal axis (twisting/tilting term) 5. creation of ζ via baroclinic processes (solenoidal term) 6. creation of ζ via frictionally induced shear

* Simplified Vorticity Equation Term A Term B • Term A: horizontal advection of absolute vorticity • Term B: convergence/divergence term *(have neglected tilting, solenoidal, and friction terms)

Relationship of Upper Level Vorticity to Divergence / Convergence DLA Fig. 8. 31 This is a key figure! Big ideas below are based on: d a/dt - divergence. + change in UL a – UL divergence -w unfavorable for cyclogenesis - change in UL a + UL divergence +w favorable for cyclogenesis

Potential Vorticity (PV) accounts for how changes in column depth are related to horizontal divergence and convergence PV is conserved if the flow is adiabatic and frictionless: → if H decreases, (ζ + f) must decrease for constant f, ζ must decrease → if H increases, (ζ + f) must increase for constant f, ζ must increase

Ice Skater Analogy

Vorticity Advection 500 mb Heights X X = positive vorticity center X = negative vorticity center (N also used)

Negative Vorticity Advection (NVA) 500 mb Hieghts (solid) Vorticity (dashed) N 14 12 08 06 Downward Vertical Motion

Positive Vorticity Advection (PVA) X 500 mb Hieghts (solid) Vorticity (dashed) 18 16 14 12 08 Upward Vertical Motion

500 mb relative vorticity Rel vort 00 Z 24 Jan 2003 +

500 mb absolute vorticity Abs vort 00 Z 24 Jan 2003 +

500 mb abs vort advection Abs vort adv 00 Z 24 Jan 2003 +

500 mb geo ht/ SLP 00 Z 24 Jan 2003 +

500 mb geo ht/ SLP 12 Z 24 Jan 2003 +

Div/Conv and vorticity tendency • Convergence of air aloft creates low level divergence (due to mass continuity)=> Downward vertical motion => The column of air in between is squashed and widened and must now spin at a slower rate (due to conservation of angular momentum) => vorticity decreases. • Divergence of air aloft creates low level convergence => Upward vertical motion => The column of air in between is stretched and made thinner and will now spin faster => vorticity increases.

Vorticity Advection and Local Vorticity Tendency • Recall that the total derivative is composed of local and advective changes in the quantity. • Local vorticity can change due to the advection of vorticity into the region, or due to DIV/CONV. • DIV/CONV is the dominant source of local vorticity changes near the surface and near the jet level, while advection is the dominate source at mid levels (near 500 mb).