EART 30351 Lecture 9 Vorticity Vorticity In two
- Slides: 12
EART 30351 Lecture 9
Vorticity •
Vorticity In two dimensions we can visualise ξ using a small paddle wheel. If the flow is rotational: T T T R<0 ξ<0 U U ξ>0 ξ<0 T T Streamlines of the flow If the flow is sheared: R>0 ξ>0 So we have rotational and shear vorticity. For synoptic-scale motion we concentrate on ξz
Components of vorticity •
Natural coordinates • n U s
Vortex stretching • Ω 2 Ω 1 h 2 r 1 r 2 Note: Ω here is the angular velocity of the cylinder, not the Earth!
Vortex stretching • • Ω 2 Ω 1 h 2 r 1 r 2 Note: Ω here is the angular velocity of the cylinder, not the Earth!
Vortex stretching • • Ω 2 Ω 1 h 2 r 1 r 2 Note: Ω here is the angular velocity of the cylinder, not the Earth!
Barotropic vorticity equation From the basic vorticity equation: Away from fronts, the tilting terms are small so Here f appears as the planetary vorticity, the vorticity existing because the Earth is spinning. ξ+f, the absolute vorticity, is the key quantity
Potential Vorticity • Ω 2 Ω 1 Δp 1 pt Δp 2 pb
Potential Vorticity • • Ω 2 Ω 1 Δp 1 pt Δp 2 pb
Potential vorticity 2 •