Scale-invariance and turbulence models for large-eddy simulation

Relationships between small and large scales of motion in turbulent flows a re of much interest in large-eddy simulation of turbulence, in which small scales are not explicitly resolved and must be modeled. This paper reviews models that are based on scale-invariance properties of high-Reynolds-numbe r turbulence in the inertial range. The review starts with the Smagorinsky model, but the focus is on dynamic and similarity subgrid models and on eva luating how well these models reproduce the true impact of the small scales on large-scale physics and how they perform in numerical simulations. Vari ous criteria to evaluate the model performance are discussed, including the so-called a posteriori and a priori studies based on direct numerical simu lation and experimental data. Issues are addressed mainly in the context of canonical, incompressible flows, but extensions to scalar-transport, compr essible, and reacting flows are also mentioned. Other recent modeling appro aches are briefly introduced.