Equilibrium and nonequilibrium statistics in inhomogeneous and unsteady turbulence

We model the turbulent kinetic energy of an arbitrary turbulent flow as an equilibrium plus a perturbation. Subsequently, perturbation theory is applied to understand the nature of both temporal and spatial fluctuations in either unsteady or inhomogeneous flows. The models are assessed using numerical simulations of the three-dimensional Kolmogorov flow. Implications for the formulation of turbulence models are discussed.