Energy balance and scale truncation of the approximate deconvolution with correction

We present the similarity theory of Approximate Deconvolution with Correction (ADC) - a member of the recently proposed family of turbulence models called LES-C. This model stems from a combination of a well-known Approximate Deconvolution Model (ADM) with a defect correction procedure. We derive the energy equality for the ADC in a way that highlights the enhanced accuracy of the ADC, as compared to the ADM. Using the proposed definitions of the ADC energy and dissipation rates, we investigate the energy cascade of the ADC; we show that it correctly predicts the energy cascade in the inertial range, and acts to dissipate the small scales at a higher rate than the ADM. The micro-scale of the ADC is then found; we prove it to be larger than the micro-scale of the ADM, which also explains the previously established efficiency of the ADC.