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lect_16

# lect_16 - Vorticity Vorticity is the microscopic measure of...

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Vorticity Vorticity is the microscopic measure of spin and rotation in a fluid. Vorticity is defined as the curl of the velocity: V r × Wind direction varies clockwise spin Wind speed varies clockwise spin Absolute vorticity (inertial reference frame): Relative vorticity (relative to rotating earth): a a V r r × ω V r r × ω

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w v u z y x k ˆ j ˆ i ˆ V = × r Expansion of relative vorticity into Cartesian components: For large scale dynamics, the vertical component of vorticity is most important. The vertical components of absolute and relative vorticity in vector notation are: relative vorticity k ˆ y u x v j ˆ x w z u i ˆ z v y w V + + = × r absolute vorticity ( ) V k ˆ r × = ζ ( ) a V k ˆ r × = η From now on, vorticity implies the vertical component (unless otherwise stated.) ( ) f sin V k ˆ e = = × φ Ω 2 r The absolute vorticity is equal to the relative vorticity plus the earth’s vorticity. Since the earth’s vorticity is For large scale circulations, a typical magnitude for vorticity is y u x v = ζ 1 5 10 = s L U ζ then and f f y u x v + = + = ζ η