Viscous-convective sub-range

In a fully developed turbulent flow,22 the scalar spectral transfer rate in the inertial-convective sub-range is equal to the scalar dissipation rate, i.e., T k) = for /cei < < Kn. Likewise, when Sc 1, so that a viscous-convective sub-range exists, the scalar trans-... 

Krt < k scalar spectral transport time scale defined in terms of the velocity spectrum (e.g., rst). 

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.

In homogeneous turbulence, spectral transport can be quantified by the scalar cospectral energy transfer rate Tap(ic, t). We can also define the wavenumber that separates the viscous-convective and the viscous-diffusive sub-ranges nf by introducing the arithmetic-mean molecular diffusivity Tap defined by... 

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