Inertial-diffusive sub-range

The form of the scalar energy spectrum for larger wavenumbers will depend on the Schmidt number. Considering first the case where Sc 1, the range of wavenumbers between kc2 and kdi is referred to as the inertial-diffusive sub-range (Batchelor et al. 1959). Note that this range can exist only for Schmidt numbers less than Scid, where... 

The form of the scalar energy spectrum in the inertial-diffusive sub-range can be found starting from the Navier-Stokes equation (see McComb (1990) for details) to be... 

As discussed in Chapter 3, with LES, the smallest scale to be resolved is chosen to lie in the inertial sub-range of the energy spectrum, which means the so-called sub-grid scale (SGS) wave numbers are not resolved. As LES can capture transient large-scale flow structures, it has the potential to accurately predict time-dependent macromixing phenomena in the reactors. However, unlike DNS, a SGS model representing interaction of turbulence and chemical reactions will be required in order to predict the effect of operating parameters on say product yields in chemical reactor simulations. These SGS models attempt to represent an inherent loss of SGS information, such as the rate of molecular diffusion, in an LES framework. Use of such SGS models makes the LES approach much less computationally intensive than the DNS approach. DNS... 

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