Turbulence lecture 18

Turbulence lecture 18 - Turbulence Lecture 18 Continuity U...

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Turbulence Lecture 18 Continuity UV W xy z ∂∂∂ ++ ∂∂ ∂ 0 0 ± s U L s V A sss VUU LL σσ   ==     AA Much smaller than s U y - momentum equation. V t 0 VV V UVW +++ 0 22 2 1 PV V V v yx y z ρ ∂∂ =− + + + 0 2 uv v xyz   ′′ −−−  0 vw Scales as / \ / / \ \ / ( ) 2 2 0 2 1 ss UU U L  A 1 (? Pressure) ( ) ( ) 2 1 vU vU L A 2 1 22 uu L   A Divide by 2 u L [] () 2 3 0 2 1 s s U U U vv pressure uL u L u uL u L                A A A For wake flows (different from jets, etc.) s uU 1 R ² argue to pressure balance with 2 v y 1
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() 2 2 2 0 1 0 P v yy P v y P P vx ρ ρρ ∂∂ ≅− =+  += integrate to get 0 Px - ambient pressure, since 2 v 0 as assume that y →±∞ 0 0 P x = 2 1 0 P v xx Streamwise momentum equation ( ) ( ) ( ) 0 s UU uuL ′′ A ±²³²´ ( ) ( ) 2 s U uL A ( ) L A / / \ U t 0 UUVU x y ++ W z
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Turbulence lecture 18 - Turbulence Lecture 18 Continuity U...

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