Vorticity The vector measure of rotation around a point Slideshow and powerpoint viewer: Mathematical Representation • Vorticity is the curl of the velocity vector • For 3-D vorticity in Cartes

Mathematical Representation • The absolute vorticity (η) is the sum of the relative vorticity (spin of the fluid) and the planetary vorticity (rotation due to the spin of the earth): f Absolute Vorticity Relative Vorticity Coriolis Parameter = 2Ωsin(Φ) where Φ = latitude

Mathematical Representation • In natural coordinates, the relative vorticity is: V V Rn n “Curvature Term” R = Radius of Curvature Vorticity due to the spin around a point “Shear Term” Vorticity due to shear of the wind

Mathematical Representation • In Cartesian coordinates (2-Dimensional): u v V x y In natural coordinates: V V V n s How the wind speed changes in the t direction Note: Convergence is just V How the wind direction changes in the n direction

The Vorticity Equation • Relates the local rate of change of vorticity to several forcing mechanisms: u v D f f Dt x y w v w u 1 2 x z y z p p x y y x Divergence Term Tilting Term Solenoidal Term Convergence = Increase in vorticity Divergence = Decrease in vorticity Represents effects on vorticity due to changes in the vertical velocity (w) in the horizontal direction Effects of pressure gradient force on changes in vorticity

Simplified Vorticity Equation • A scale analysis shows that the tilting and solenoidal terms are much smaller than the other terms • Furthermore, break the total derivative into its local change and advective components to yield: u v V ( f ) ( f )( ) t x y Advection of absolute vorticity Divergence term