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

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Unformatted text preview: 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 V r r w v u z y x k j i 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 y u x v j x w z u i z v y w V + + = r absolute vorticity ( ) V k r = ( ) a V k r = From now on, vorticity implies the vertical component (unless otherwise stated.) ( ) f sin V k e = = 2 r The absolute vorticity is equal to the relative vorticity plus the earths vorticity. Since the earths vorticity is For large scale circulations, a typical magnitude for vorticity is y u x v = 1 5 10 = s L U then and f f y u x v + = + = Circulation and Vorticity The relationship between relative vorticity and circulation can be seen by considering the following expression, in which we...
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This note was uploaded on 10/25/2011 for the course ENVSCI 324 taught by Professor Broccoli during the Spring '11 term at Rutgers.

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

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