  We study mathematical and physical properties of a family of recently
introduced, reduced-order approximate deconvolution models. We first show a
connection between these models and the NS-Voigt model, and that NS-Voigt can
be re-derived in the approximate deconvolution framework. We then study the
energy balance and spectra of the model, and provide results of some turbulent
flow computations that backs up the theory. Analysis of global attractors for
the model is also provided, as is a detailed analysis of the Voigt model's
treatment of pulsatile flow.
