Existence of the intermediate scalar-spectrum subrange

Determine whether the scalar-spectrum subrange described by Eq. (29) exists as a physically observable scaling regime, given that its bandwidth may be very limited and that its spectrum may be obscured by the exponential scalar-dissipation term.

Background

The paper derives several scalar-spectrum subranges for momentum–scalar coupled turbulence with anomalous momentum and scalar diffusion. In the second subrange considered in Section 4, the authors obtain a theoretical scalar spectrum in the regime where the relevant scalar-transfer and diffusion terms balance. Although the derived spectrum could theoretically extend to high wavenumber, the authors note that its bandwidth may be extremely narrow and that the spectrum may be masked by exponential decay from scalar dissipation. They therefore leave unresolved whether this predicted subrange actually exists as a distinguishable regime.