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By using Direct Numerical Simulations (DNS) of bubbly flows with passivescalars, we show a transition in the scalar spectra from a $k^{-5/3}$ to a$k^{-3}$ scaling with the wavenumber $k$, in contrast with those ofsingle-phase isotropic turbulence. For cases with a mean scalar gradient in thehorizontal direction, the scalar spectrum decays faster than $k^{-3}$ at highwavenumbers. While the $k^{-3}$ scaling is well established in the bubbly flowvelocity spectrum, the scalar spectrum behaviour is not fully understood. Wefind that the transition length scale of the scalar spectra is comparable to orbelow the bubble diameter and decreases with the molecular diffusivity of thescalar in the liquid. We use DNS to compute the scalar spectra budget and showthat the scalar fluctuations are produced by the mean scalar gradient at lengthscales above the bubble diameter, contrary to the velocity fluctuations. Atlength scales below the bubble diameter, the net scalar transfer scales as$k^{-1}$ inducing the $k^{-3}$ scaling of the scalar spectra. This finding isconsistent with the hypothesis proposed by Dung et al. (2023) about thephysical mechanism behind the $k^{-3}$ scaling. We also show dependencies ofthe bubble suspension's convective scalar diffusivity on the gas volumefraction and molecular diffusivity that differs based on the direction of themean scalar gradient. For a mean scalar gradient in the vertical direction, wefind and qualitatively explain a significant effect of the moleculardiffusivity in the gas on the convective scalar diffusivity.

Assessing passive scalar dynamics in bubble-induced turbulence using DNS