Structure Functions and Spectra of Scalar Quantities in the Inertial–Convective and Viscous–Convective Ranges of Turbulence

Abstract

The Obukhov–Corrsin constants (often referred to as Kolmogorov constants) are the constants of proportionality in formulas pertaining to the inertial-convective range of structure functions (or spectra) of scalar quantities and the cross-structure functions (or cospectra) of pairs of scalar quantities. These Obukhov–Corrsin constants are shown to be equal for all scalar quantities and pairs of scalar quantities. The inertial-convective and viscous-convective range formulas for cross-structure functions (or cospectra) can be deduced from those of the structure functions (or spectra). Special attention is given to the case of dimensionless scalar quantities like refractive index for which the inertial-convective and viscous-convective range formulas can be deduced by several different arguments. Dimensional analysis is useful for the structure functions, cross-structure functions, spectra and cospectra of the inertial-convective range and for the spectra and cospectra in the viscous-convective range. The structure and cross-structure functions do not possess viscous-convective ranges distinct from their viscous-diffusive ranges, however, and dimensional analysis gives incorrect results in this case.