Energy-containing range scalar

The scalar integral scale characterizes the largest structures in the scalar field, and is primarily determined by two processes (1) initial conditions - the scalar field can be initialized with a characteristic that is completely independent of the turbulence field, and (2) turbulent mixing - the energy-containing range of a turbulent flow will create scalar eddies with a characteristic length scale I.,p that is approximately equal to Lu. 

Note that as Re/, goes to infinity with Sc constant, both the turbulent energy spectrum and the scalar energy spectrum will be dominated by the energy-containing and inertial/inertial-convective sub-ranges. Thus, in this limit, the characteristic time scale for scalar variance dissipation defined by (3.55) becomes... 

Figure 4.8. Sketch of wavenumber bands in the spectral relaxation (SR) model. The scalar-dissipation wavenumber kd lies one decade below the Batchelor-scale wavenumber kb. All scalar dissipation is assumed to occur in wavenumber band [/cd, oo). Wavenumber band [0, k ) denotes the energy-containing scales. The inertial-convective sub-range falls in wavenumber bands [k, k3 ), while wavenumber bands [/c3, /cD) contain the viscous-convective sub-range.

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