Vorticity Vertical component of vorticity: i.e., the rotation about the local vertical There are three types of vorticity used in geophysical fluid dynamics If the wind is geostrophic, the geostrophic relative vorticity is given by

Vorticity y + + x

Divergence Divergence: From the continuity equation - For incompressible flow: Most meteorologists simply use divergence when they mean the horizontal divergence

Divergence

Vorticity and Divergence Why they are important? What’s the unit? What’s the order of the magnitude? Relative Vorticity (Synoptic Scales) Why?

Vorticity and Divergence (Synoptic Scale) Relative Vorticity Same signs for both terms

Vorticity in Nature Coordinates Curvature effect S n V Shear effect - The smaller the R (i.e., curved more, shorter waves), the stronger the curvature term. R is positive for cyclonic circulation and negative for anti-cyclonic circulation.

Vorticity ? curvature Shear

Vorticity Advection L V wind speed Trough Ridge Relative vorticity Planetary vorticity advection

Vorticity Advection (shorter Rossby waves) L V Trough Ridge PVA Postive Vorticity Advection Wavelength (PVA)

Vorticity Advection (shorter Rossby waves) PVA (assume wave solution) z decreases with time ascent divergence aloft convergence PVA Adiabatic cooling

Vorticity Advection (shorter Rossby waves) L V Trough Ridge Divergence PVA

Vorticity Advection (shorter Rossby waves) L V Trough Ridge Con. Div. NVA PVA Waves propagate eastward!

Vorticity Advection (shorter Rossby waves) NVA (assume wave solution) z increases with time decent convergence aloft divergence NVA Adiabatic warming

Vorticity Advection (shorter Rossby waves) wave speed C 564 570 576 PVA NVA Trough Wave propagation speed Tropopause z level of non-divergence 500-600 mb speed U C

H L Vertical Coupling PVA NVA Tropopause level of non-divergence wave speed C 564 570 576 PVA NVA Trough z speed U C Tropopause level of non-divergence 500-600 mb H L Will grow Will grow

Low-level cyclone and 500mb heights 5520 5460 direction of propagation L warm air mass cold air mass warm front cold front 996 992 988 ** 32 31 .. 39 37 49 46 . 56 52 Upper and low-level coupled together – upper level trough enhances the low-level cyclone development.

Low-level cyclone and 500mb heights 5520 5460 5520 5460 L upper level trough catches low-level system – low level system is decaying. upper level trough is about to catch low-level system.