Scale Truncation and the Energy Balance of the ADC
Alexander E. Labovsky · 2025
Continuing the discussion of the ADC model from Chapter 7 , the scale similarity theory of the ADC is presented in Chapter 8 . This includes the discussion on the different views of the energy balance inequality – in terms of the “original” velocity field and the filtered velocity that is the quantity of interest in case of the ADM. This leads to a deeper understanding of the extra terms in the right-hand side of the ADC: instead of dismissing them as extra forcing, one can incorporate these terms into the energy balance equation and notice the effects of these terms on the kinetic energy spectrum of the ADC. Chapter 8 provides the theoretical explanation to the numerical results of Chapter 7 , where the ADC was shown to outperform the ADM. It is shown in Chapter 8 that both the ADM and the ADC correctly predict the energy cascade in the inertial range, but the ADC dissipates the subgrid scale energy more efficiently, than the ADM. This difference in the secondary energy cascades is the reason for the increased efficiency of the ADC, with its microscale being much larger than that of the ADM.