Differential diffusion and spectral transfer in turbulent mixing at high Schmidt numbers

Many applications of turbulent mixing involve differential diffusion between scalars of different molecular diffusivities. We study this phenomenon using direct numerical simulation, employing a dual-grid computational approach to meet stringent resolution requirements for scalars of low diffusivity (high Schmidt number, $Sc$). The largest Schmidt number ratio considered is 64, occurring between two scalars of $Sc=4$ and 256, whose fluctuations are produced by velocity fluctuations acting upon a uniform mean scalar gradient. Spectral transfer characteristics examined individually for each scalar show robust evidence of a forward cascade, where local transfer by nonlocal interactions modulated by low-wavenumber velocity modes is readily observed at the small scales. Contributions to the coherency spectra from moderately non-local velocity-scalar triads were found to produce a net decorrelating effect at small scales which is balanced by the coherent mean gradient forward cascade leading to a stationary state. The scalings of the two-scalar difference spectrum and joint dissipation rate are investigated in detail. The role of differential diffusion in double-diffusive convection is briefly addressed.