Lecture-8

# vi 4 j l 0 v j l q i j g t vorticity

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Unformatted text preview: VI lù Q ! q, ~ s: '; ~ VI IJ - v 1 . :: ~ \/' l " ~ - \L .. ~ ~ - Vi 4 € J /" L. . ,.. 0 V' .. ~ j- l Q )- '- I.. \J - G t Vorticity Dynamics (Remember the importance of viscosity.) . J t ~ 0 ~ (U 'Û .j ~ -i vA \~ Q II . I~ ~ .J -: :i -. II ,~ ../ () ,J '.. lÙ lL ù "= F lrJ 'J 't )~ )- ~ - ~ 'C 1.. ~ ~ f- ~ 'I \ c: VECTOR IDENTITIES4 J (1) A · B × C = A × B · C = B · C × A = B × C · A = C · A × B = C × A · B Il\ ~ ~ , l/ I :: (\ ~ 'X I\: Z r- 1:5 l~ "- I~\~ (2) A × (B × C) = (C × B) × A = (A · C)B − (A · B)C r¡r- -i \ i :J ~ i~ -If' "t I :: (' ~ , + (V ~ I ~ '-,f' ~ ~ L b. i I tr II 13' 'j l~ + 1"3 \-. (" ~ L X 1/ -l-a Notation: f, g, are scalars; A, B, etc., are vectors; T is a tensor; I is the unit dyad. '\ y. ~ + ~ (3) A × (B × C) + B × (C × A) + C × (A × B) = 0 (4) (A × B) · (C × D) = (A · C)(B · D) − (A · D)(B · C) . ~~ × (f A) = f ×A+ (9) · (A × B) = B · ×A−A· (10) × (A × B) = A( · B) − B( (gf )...
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## This document was uploaded on 02/28/2014 for the course PHYS 4200 at Columbia.

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