The turbulent transport of small particles (dust particles, cloud droplets, etc.) can be viewed macroscopically as a problem of passive scalar turbulence with extremely high Schmidt numbers. To investigate the spectrum of a passive scalar carried by such particles, we conducted Lagrangian particle simulations in homogeneous isotropic turbulence. The scalar variance spectrum obeys the -5/3 and -1 power laws in the lower and higher wavenumber ranges, respectively, with a clear transition at normalized wavenumber of about 0.04. The dimensionless constants for each range are also consistent with the estimations obtained from previous laboratory and simulation studies.
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Saito et al. (2024) studied this question.
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