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Unformatted text preview: Tony Burden’s Lecture Notes on Turbulence, Spring 2007 Chapter 3. Thin Shear Layers and Free Shear Flows 3a Thin-shear-layer Equations examples — free shear flows, such as jets, wakes and mixing layers, and wall- bounded flows, such as boundary layers and wall jets. empirical observation; ∂U ∂x ∂U ∂y . Order-of-magnitude estimates Let U ∼ U , ∂U ∂x ∼ Δ U L and ∂U ∂y ∼ Δ U δ . Then, ∂U ∂x ∂U ∂y → δ L. See the next section for examples of the velocity scales U and Δ U . Statistically stationary and two-dimensional flow field, The two-component, two-dimensional velocity is, U ( x, y ) , V ( x, y ) , . The Reynolds stress is, - ρ h u 2 i - ρ h u v i- ρ h u v i - ρ h v 2 i- ρ h w 2 i , and depends only on x and y . All the components are assumed to have the same order of magnitude, h u i u j i ∼ u 2 T . the continuity condition and the transverse component of velocity ∂U ∂x + ∂V ∂y = 0 → V ∼ δ L Δ U Δ U....
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This note was uploaded on 09/16/2011 for the course ME 563 taught by Professor Staff during the Spring '11 term at Auburn University.
- Spring '11