Vorticity Objectives Define Vorticity Earth and Relative vorticity
Vorticity Objectives • Define Vorticity – Earth 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
Relative Shear Vorticity
Relative Curvature Vorticity
Vorticity is the measure of spin of an air parcel
Earth Vorticity ( f ) • 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 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 divergence (stretching) 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: 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
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).
Vorticity Advection 500 mb X X = positive vorticity center X = negative vorticity center (N also used)
Positive Vorticity Advection (PVA) X 18 16 14 12 08 Upward Vertical Motion
Negative Vorticity Advection (NVA) N 14 12 08 06 Downward Vertical Motion
Rel vort 00 Z 24 Jan 2003 + 500 mb relative vorticity
Abs vort 00 Z 24 Jan 2003 + 500 mb absolute vorticity
Abs vort adv 00 Z 24 Jan 2003 + 500 mb abs vort advection
SLP 00 Z 24 Jan 2003 + 500 mb geo ht/ SLP
SLP 12 Z 24 Jan 2003 + 500 mb geo ht/ SLP
- Slides: 24