Second-moment closure: present… and future?

Abstract The paper summarizes the present position of second-moment closure and outlines possible directions for future development. It is first argued that a simple form of second-moment treatment that has been widely used for computing industrial flows gives demonstrably superior predictive accuracy that any eddy—viscosity model. More complex schemes, now in the final phases of development, that exactly satisfy various limiting constraints, give a further marked improvement in our ability to mimic the response of turbulence to external inputs. The inclusion of such models into commercial software over the next few years is quite feasible. The desirability of introducing a further second-rank tensor into the closure is considered; the conclusion reached is that, for most applications, the likely benefits would not justify the additional effort. The split-spectrum approach may, however, be attractive for certain flows with unusual spectral distributions of energy. The introduction of a second scale-related equation is arguably a more sensible approach since the extra computational cost is small while the added flexibility could bring significant benefits in modeling turbulence far from equilibrium.