Vorticity and Jets

1. METR 2413 12 April 2004 Vorticity and Jets

2. Review from quiz Review Hydrostatic balance Vertical pressure gradient force Scale, g ~ 10 m/s2, vertical pgf ~ 10 m/s2 Horizontal pressure gradient force balanced by Coriolis force f ~ 10-4 s-1, v ~ 10 m/s, Coriolis force ~ 10-3 m/s2 ρ ~ 1 kg/m3, Δp ~ 10 hPa ~ 1000 Pa, Δx ~ 1000 km ~ 106 m

3. Review from quiz Thermal wind In the presence of a horizontal temperature gradient, the tilt of pressure surfaces increases with height. p=p2 ug Δz p=p1 North cold warm Zonal wind increases with height in the NH because temperature decreases towards the pole, giving increasing poleward height gradients.

5. Circulation and Vorticity: Two primary measures of rotation in a fluid By convention, both circulation and vorticity are positive in the counterclockwise direction (cyclonic in the Northern Hemisphere) Circulation: Macroscopic measure of rotation for a finite area of the fluid = integration of the tangential component of velocity around a closed path Vorticity: The tendency to spin about an axis; Microscopic measure of rotation at any point in the fluid

6. The tighter the spin, the larger the magnitude of the vorticity • On Earth there is: • Vorticity from Earth’s spin (planetary vorticity) • “Local” vorticity due to cyclonic/anticyclonic motion (relative vorticity)

7. Absolute vorticity (total vorticity): • measured with respect to the fixed stars • includes Earth’s rotation (planetary vorticity) and rotation of atmosphere relative to Earth’s surface (relative vorticity) • angular momentum is conserved, so absolute vorticity is also conserved for frictionless motion • ζa = ζr + fc = constant • where fc is the Coriolis parameter = 2Ω sinΦ (planetary vorticity)

8. Relative vorticity: • measure of the rotation of the atmosphere about a vertical axis relative to Earth’s surface • units of sec-1 • Synoptic scale vorticity is analyzed and plotted on the 500 mb chart • 500 mb vorticity may be referred to as “vertical vorticity” (the spin is in relation to the vertical axis) • The vertical component of vorticity can be expressed as: • ζr = ∂v/∂x – ∂u/∂y

9. Typical magnitude of the relative vorticity for synoptic scale flow, U ~ 10 m/s, L ~ 1000 km ζ = ∂v/∂x - ∂u/ ∂y ≤ U/L ~ 10-5 sec-1 Typical magnitude of planetary vorticity f ~ 10-4 s-1

10. We’ve seen that relative vorticity is non-zero for two reasons: • Either streamlines of wind have curvature, or • The wind field has horizontal shear (or both) Curvature vorticity: positive in troughs and negative in ridges

11. Positive and negative relative shear vorticity can be due to variations in westerly wind speed with latitude slow Positive shear vorticity fast fast Negative shear vorticity slow Think of the above air flows as wide rivers – if you put a log oriented north-south in the flow, the log would turn counterclockwise on the top, and clockwise on the bottom because of the shear

12. Positive vorticity advection (PVA) • found where air blows from regions of higher vorticity toward lower vorticity • significant because main mechanism to reduce vorticity is divergence • that is, in regions of PVA there tends to be divergence, which implies upward motions beneath these areas, surface convergence and surface pressure falls • Negative vorticity advection (NVA) • found where air blows from regions of lower vorticity towards higher vorticity • main mechanism to increase vorticity is convergence • when there is NVA in upper levels, there tends to be downward motion below, surface divergence and surface pressure rises

13. Low Vorticity Low Vorticity Upper Level Convergence High Vorticity Anticyclonic Vorticity Advection - Moving from low vorticity to high vorticity requires convergence aloft.

14. Jet streaks • Jet streaks are localized regions of very fast winds embedded within the jet stream. Sometimes these local wind maxima reach speeds in excess of 160 knots. • Jet streaks are important as they are indicative of rising motion/falling pressures at the surface. The figure below represents an idealized jet streak.

15. Height contour As air enters from the left, it must be accelerated as the height contours are closer together and the pressure gradient force is stronger. The stronger pgf causes an ageostrophic flow to the north, leading to convergence to the north and a divergence to the south. As a result, air sinks in the northern 'quadrant', and rises in the southern quadrant of a jet entrance. The force to accelerate the flow to the east is supplied by the Coriolis force as air flows from the south to the north near the jet entrance, leading to a force to the east (the right). Entrance Region (Rear) Exit Region (Front)

16. In the jet exit region, the opposite happens, as air flows from north to south to create the force necessary to decelerate the air as it leave the jet streak. The vertical motion resulting from this leads to rising air in the north quadrant and sinking air in the south of the jet exit.

17. CONV DIV However, not all jet streaks are straight. In fact, most are curved. The ageostrophic flow and anticyclonic vorticity advection cause convergence in the left entrance of the jet and the ageostrophic flow and the cyclonic vorticity advection cause divergence in the left exit region The divergence and ascent ahead of the upper level trough enhance the development of surface lows Exit Region (Front) Entrance Region (Rear)

18. Summary • Vorticity is a measure of the local rotation in a fluid • Planetary vorticity due to the rotoation of the earth • Relative vorticity due to the rotation of air relative to the surface, curvature vorticity and shear vorticity • Absolute vorticity = planetary vorticity + relative vorticity is conserved in the atmosphere • Positive (cyclonic) vorticity advection leads to upper level divergence, and rising motion • Jet streaks are localized regions of very strong winds, with poleward motion at the jet entrance and equatorward flow at the jet exit • Enhanced divergence at the left exit region of a cyclonic curved jet, enhances development of surface low