Approximating the larger eddies in fluid motion V: Kinetic energy balance of scale similarity models

We first review a classical scale-similarity model used to simulate the motion of large eddies in a turbulent flow. The kinetic energy balance of this model is very unclear in theory. Experiments with it often have reported that an additional Smagorinski type subgridscale term is needed. This term is not benign; it can alter significantly the predicted long term dynamics of the large eddies. However, we also show that the principal of scale-similarity (introduced in 1980 by Bardina, Ferziger and Reynolds) can also give rise to other scale similarity models which have the correct kinetic energy balance.