Turbulence lecture 14

Turbulence lecture 14 - Turbulence Lecture 14 Vorticity...

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Turbulence Lecture 14 Vorticity Dynamics - Important aspect of Turbulence - Vorticity Turbulence is characterized by very high rates of fluctuating vorticity - Vortex tube stretching is key non-linear effect - 2-D flows don’t have this feature 2 11 22 ij ij ij ij j ii i jj i j sr vs s u uu u j i u x xx ε =  ∂∂ =+ +−  ∂ ∂  ±²²³ ² ² ´±² ²³ ² ²´ Symmetric strain rate Anti-symmetric rotation or vorticity tensor ij r - 3 independent components i ijk jk r ω =− or 1 2 ij ijk k r εω Note: A vector cross product can be written in suffix notation, by using the alternating symbol (or Levi-Civita symbol). 1, ( , , ) ( __ _ _ _ __ _ _ _ __ ,,) 0, ijk if i j k are cyclic if i j k are anti cyclic otherwise Cyclic – 1, 2, 3; 2, 3, 1; 3, 1, 2 Anticyclic - 3, 2, 1; 1, 3, 2; 2, 1, 3 Otherwise 2 suffixes are the same.
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2 2 2 ii j i j ij ij ij ij i j ij rr ss uu xx ω = −= ∂∂ Scaling Terms 2 2 ij ij u λ where is the Taylor microscale, since 2 2 2 22 2 2
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This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.

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Turbulence lecture 14 - Turbulence Lecture 14 Vorticity...

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