Application of Turbulence Model Equations to Axisymmetric Wakes

The second-order invariant modeling technique for turbulent flows as developed by Donaldson is applied to axisymmetric wakes. All empirical model parameters are chosen from data on jets and shear layers leaving the wake completely determined as a function of initial conditions. Model predictions for the mean velocity distribution and the distributions of the four components of the second-order stress tensor are verified by comparison with the experimental observations of Chevray for a wake with significant mean momentum and Naudascher for the wake behind a self-propelled body. Nomenclature a, b = model constants defined in Eq. (12) D = diameter of the generating body M = normalized momentum defect in the wake, see Eq. (15) p = pressure q = square root of twice the turbulent kinetic energy per unit mass r = radial coordinate r* = radius at which 1/2 reaches one half its maximum