Lagrangian Perspectives on Mixing and Turbulent Diffusivity in Stratified Shear Flows

Speaker: Andrew Zhou, DAMTP
Series: Engineering Fluids Group Seminar

We investigate turbulent mixing in stably stratified shear flows using Lagrangian particles in direct numerical simulations (DNS), focusing on flows susceptible to Kelvin–Helmholtz instability (KHI) and Holmboe wave instability (HWI). By tracking particles along their trajectories, we first examine how these instabilities produce distinct mixing behaviours, providing a complementary view of the conventional distinction between the mixing by ‘overturning’ associated with KHI and mixing by ‘scouring’ associated with HWI. We then develop a Lagrangian approach to diagnosing irreversible mixing in a buoyancy-sorted coordinate, following the framework of Winters and D’Asaro (1996). This approach enables the analysis of mixing for weakly diffusive tracers with high Schmidt numbers, which are difficult to resolve directly in DNS. We further investigate whether the evolution of a passive tracer in buoyancy-sorted coordinates can be inferred from the effective diffusivity diagnosed from the density field. We find that this inference works well when the tracer and density have the same molecular diffusivity, but an additional ‘tracer eddy term’ due to correlations between tracer fluctuations and buoyancy can become important otherwise. Finally, we show that mixing induced by KHI can be appropriately modelled using a constant diffusivity, whereas HWI requires an empirically determined diffusivity that varies in space and time.