A similarity theory of approximate deconvolution models of turbulence

We apply the phenomenology of homogeneous, isotropic turbulence to the family of approximate deconvolution models proposed by Stolz and Adams. In particular, we establish that the models themselves have an energy cascade with two asymptotically different inertial ranges. Delineation of these gives insight into the resolution requirements of using approximate deconvolution models. The approximate deconvolution model's energy balance contains both an enhanced energy dissipation and a modification to the model's kinetic energy. The modification of the model's kinetic energy induces a secondary energy cascade which accelerates scale truncation. The enhanced energy dissipation completes the scale truncation by reducing the model's micro-scale from the Kolmogorov micro-scale.