Differential diffusion and active-scalar turbulence at high Schmidt numbers

Recent progress inn GPU-optimized algorithm development (Clay {\em et al.} Comput. Phys. Commun., 2018) has provided a new capability to study turbulent mixing at high Schmidt numbers with demanding resolution requirements. Here we consider both passive and active scalars. Differential diffusion of passive scalars is studied in Schmidt number regimes comparable to those of temperature and salinity (7 and 700) in the ocean. The correlation between fluctuating gradients of the different scalars agrees well with a semi-empirical formula motivated by past simulation data at more modest Schmidt numbers. For active scalars our primary interest is in modifications of the turbulence structure due to one or two scalars with uniform mean gradients in the vertical, with their dynamical effects representable by Boussinesq-type terms in the equations of motion. An active scalar of higher Schmidt number is seen to have a stronger effect on small-scale statistics, such as oscillating mean-square vorticity components in a horizontal plane, although some form of saturation of these effects at sufficiently high Schmidt number is possible. The largest simulations to be presented will be at $8192^3$ grid resolution.