The geometry of mixing in stratified flows: theory, experiments, observations and simulations
The world's oceans are stably stratified in density. They are also often turbulent. Turbulence, which stirs reversibly the oceans on relatively large scales, can enhance the rate at which parcels with different densities irreversibly mix. Mixing is a process that happens on (very) small scales but is known to have a leading order impact on large-scale ocean circulation, for example. Quantifying the rate at which turbulence mixes density differences is therefore crucial. However, it is still an area of great uncertainty. How does the inherent small- and large-scale structure of stratified turbulent flows affect their mixing properties? What is the role of the smallest scales of the flow and more precisely of the molecular properties of the scalar being mixed? Can a geometric approach to stratified turbulent flows, based on the kinematics, dynamics and subsequent dissipation of relevant density structures help us build a comprehensive picture of mixing in such flows? This thesis aims to provide insight into these questions. A segmentation methodology extracting density structures (namely `interfaces' and `lamellae') in a characteristic `layered' stratified turbulent flow is developed in chapter 2. This methodology is applied to fully-resolved, three-dimensional direct numerical simulation data at various Prandtl numbers (quantifying the ratio of the molecular viscosity to molecular diffusivity of the scalar being mixed). In particular, we show how the geometric structure of the turbulent density field explains the empirically observed property that the `mixing efficiency' of a stratified flow decreases as the Prandtl number increases. Such segmentation of the density field calls for the experimental and numerical study of the extracted density structures in both isolation and combination. This programme is carried out in chapter 3: an isolated lamella is studied experimentally in an idealised (laminar) flow and a mixing efficiency criterion based on the structure's stretching, settling and diffusion is developed. In chapter 4 the experimental findings are extended to the turbulent case using ideas from stochastic processes. In particular, the problem of (Lagrangian) tracer dispersion in stratified turbulent flows is analysed. While our focus was on relatively small scales in chapters 2, 3 and 4, the last two chapters of the thesis examine the larger (ocean basin) scales. More precisely, we analyse potential spatial biases arising from commonly used large-scale ocean mixing parameterisations in chapter 5. Finally, in chapter 6, we develop a model for the formation of (or lack thereof) density staircases — a large-scale density structure commonly observed in the Arctic ocean and Mediterranean Sea — in stratified and sheared turbulent flows.
Fluid Mechanics, Mixing, Stratified turbulent flows
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