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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 - x 2 4 at 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 flow 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. For the velocity of the particles holds: v ( t ) = v + v ( t ) with v ( t ) = 0 . The Navier-Stokes equation now becomes: v t + ( v · ) v = - p + ν 2 v + div S R where S Rij = - v i v j is the turbulent stress tensor. Boussinesq’s assumption is: τ ij = - v i v j . It is stated that, analogous to Newtonian media: S R = 2 ν t D . Near a boundary holds: ν t = 0 , far away of a
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