Chapt06

Reynolds idea was to split each property into mean

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Unformatted text preview: to Eqs. (6.7), and take the time mean of each equation. The continuity relation reduces to u x y w z 0 (6.13) which is no different from a laminar continuity relation. However, each component of the momentum equation (6.7b), after time averaging, will contain mean values plus three mean products, or correlations, of fluctuating velocities. The most important of these is the momentum relation in the mainstream, or x, direction, which takes the form du dt p x y gx u y x u u x u z 2 u z (6.14) uw | v v u 2, u , and u w are called turbulent stresses The three correlation terms because they have the same dimensions and occur right alongside the newtonian (laminar) stress terms ( u/ x), etc. Actually, they are convective acceleration terms (which is why the density appears), not stresses, but they have the mathematical effect of stress and are so termed almost universally in the literature. The turbulent stresses are unknown a priori and must be related by experiment to | e-Text Main Menu | Textbook Table of C...
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