Explicit algebraic Reynolds stress and non-linear eddy-viscosity models

This article reviews explicit algebraic Reynolds stress models and other non-linear eddy-viscosity turbulence models utilised in the context of Reynolds-Averaged Navier-Stokes simulations of turbulent flows. Since the 1990s, these modelling classes have become important intermediate classes between the linear eddy viscosity models and full Reynolds stress transport models. The derivation of explicit algebraic Reynolds stress models from the Reynolds stress transport models, and the required simplifications are discussed. The most important simplification is the weak-equilibrium assumption. Properties of the basic weak-equilibrium assumption and its extended form are discussed. Differences between explicit solutions based on complete tensor representation and those based on reduced representation as well as other non-linear eddy-viscosity models are pointed out. The scale-determining models are also discussed briefly.