This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
This note was uploaded on 10/25/2011 for the course ENVSCI 324 taught by Professor Broccoli during the Spring '11 term at Rutgers.
 Spring '11
 Broccoli

Click to edit the document details