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 Show the mathematical representation of relative vorticity: Both in vector form, derivative form, and natural coordinates (shear and curvature terms): Show examples of shear and curvature 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 Draw picture of NH on the board, show CCW spinning earth. Show how the spin is max about the vertical axis at the pole, min at the equator. They may confuse vorticity with coriolis force. Objects do not have to be in motion to have vorticity Write the equation for earth vorticity on the board.

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). Write equation for absolute vorticity

Relative Vorticity and Earth Vorticity In this figure, the subscript e (r) indicates Earth (relative) vorticity. DLA Fig. 8.28

advection of relative ζ Vorticity Equation 1 2 3 4 5 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) creation of ζ via baroclinic processes (solenoidal term) 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

PV is conserved if the flow is adiabatic Potential Vorticity 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 Draw the cylinder picture on the board and talk through it. Next slide summarizes

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. Show angular momentum equation – this concept is just conservation of mvr. Note also that there must be a net div (conv) in the entire column for pressures to fall (rise) at the surface, otherwise the converging (diverging) air at the surface would cause pressures to rise (fall). You’ll talk more about this in trop and strat.

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). Show equation with advection, and how to determine whether advection is + or -. Also show how local change can be zero if the div offsets the advection.

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

Upward Vertical Motion Positive Vorticity Advection (PVA) X 18 16 14 12 08 Upward Vertical Motion

Downward Vertical Motion Negative Vorticity Advection (NVA) N 14 12 08 06 Downward Vertical Motion

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

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

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

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

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