Differential Diffusion in Breaking Kelvin–Helmholtz Billows

Abstract

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 Reb and of the density ratio Rρ (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 Reb and also with increasing Rρ. Instantaneous diffusivity ratios near unity are achieved during the most turbulent phase of the event even when Reb is small; much of the Reb dependence results from the fact that, at higher Reb, 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 Reb exceeds O(102). The effect of Rρ is significant only when Reb is less than this value.