Differential diffusion in breaking Kelvin-Helmholtz billows

Direct numerical simulations are used to compare turbulent diffusivities of heat and salt during the growth and collapse of Kelvin-Helmholtz billows. The ratio of diffusivities is obtained as a function of buoyancy Reynolds number Re-b and of the density ratio R-rho (the ratio of the contributions of heat and salt to the density stratification). The diffusivity ratio is generally less than unity (heat is mixed more effectively than salt), but it approaches unity with increasing Re-b and also with increasing R-rho. Instantaneous diffusivity ratios near unity are achieved during the most turbulent phase of the event even when Re-b is small; much of the Re-b dependence results from the fact that, at higher Re-b, the diffusivity ratio remains close to unity for a longer time after the turbulence decays. An explanation for this is proposed in terms of the Batchelor scaling for scalar fields. Results are interpreted in terms of the dynamics of turbulent Kelvin-Helmholtz billows, and are compared in detail with previous studies of differential diffusion in numerical, laboratory, and observational contexts. The overall picture suggests that the diffusivities become approximately equal when Re-b exceeds O(10(2)). The effect of R-rho is significant only when Re-b is less than this value.