On the behavior of two-equation models at the edge of a turbulent region

Abstract

The flow structure predicted in the vicinity of free-stream edges by two-equation eddy-viscosity turbulence models is examined. Analytical expansions, previously used by several authors, are shown to be weak solutions to the pure nonlinear diffusion problem, connecting with trivial solutions in the nonturbulent region. They remain locally valid solutions to the full one-dimensional system of model equations in the vicinity of the edge, provided that some constraints on the turbulent ‘‘Prandtl numbers’’ are satisfied. Calculations performed with the (k,ε) turbulence model for a time-evolving mixing layer and a flat-plate boundary layer in zero pressure gradient are fully consistent with the analysis. In contradiction of a prior study by Lele [Phys. Fluids 28, 64 (1985)], the modeled turbulent-kinetic-energy, dissipation-rate, and shear-stress fronts are found to propagate into the nonturbulent region at the same velocity, with no need for any special relationship between the model constants. Implications related to the calibration of models are discussed.