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44 Physics Formulary by ir. J.C.A. Wevers with D = ± 2 κ / ω± c . At x = π D the temperature variation is in anti-phase with the surface. The one- dimensional solution at Φ =0 is T ( x, t )= 1 2 π at exp ² - x 2 4 at ³ This is mathematical equivalent to the diffusion problem: n t = D 2 n + P - A where P is the production of and A the discharge of particles. The Fow density J = - D n . 9.9 Turbulence The time scale of turbulent velocity variations τ t is of the order of: τ t = τ Re / Ma 2 with τ the molecular time scale. ±or the velocity of the particles holds: v ( t )= ± v ² + v ± ( t ) with ± v ± ( t ) ² =0 . The Navier-Stokes equation now becomes: ± ² v ² t +( ± ² v ² · ) ± ² v ² = - ∇± p ² ± + ν 2 ± ² v ² + div S R ± where S Rij = - ± ± v i v j ² is the turbulent stress tensor. Boussinesq’s assumption is: τ ij = - ± ´ v ± i v ± j µ . It is stated that, analogous to Newtonian media: S R =2 ±ν t ± D ² . Near a boundary holds:
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

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