Mixing processes and buoyancy transport in stratified turbulent flows

Abstract

This thesis attempts to increase the overall understanding of turbulent mixing by exploring the controls on the vertical buoyancy transport in a stratified turbulent Taylor-Couette flow. The inner cylinder of the tank, of radius R1, rotates, while the outer cylinder, of radius R2, is fixed, and the gap \Delta R=R2-R1 is filled with fluid up to a depth H, so that the aspect ratio H/ \Delta R=2.7-2.8. To simulate the global overturning circulation that perpetually carries and redistributes heat, salt and carbon between ocean basins at different rates, we conduct a series of experiments where we vary the rotation of the inner cylinder, \Omega. In addition, we model rainfall and ice melting on the ocean surface by supplying a fresh water flux at the top of the tank, while the dense currents released by ice formation at the Antartica are modeled by a saline water flux supplied at the base of the tank. At the same time, we vent the same flux as the supply by two sinks located at the same depth of the respective sources. In our stylized experiments, the diapycnal mixing through isopycnal surfaces can be associated to the salt flux extracted at the top, whereas the upwelling flux can be measured by the fluid extracted at the bottom. In our experiments, we also vary the salinity of the bottom source, in order to simulate different interglacial periods. Firstly, we found that in the unsaturated regime, the vertical buoyancy flux is rate-limited by the salinity of the bottom source and it depends linearly on the buoyancy frequency, N, while in the saturated regime, it is rate-limited by turbulence, it is independent on N and proportional to \Omega^3, matching the equivalent flux through a two-layer or multi-layer stratification, or through the interfaces that spontaneously form in a linear stratified fluid, for sufficiently high initial stratification. In this thesis, we will also discuss the influence of the initial condition and of the position of the sources and sinks on the steady-state stratification, as well as the effects of a coupling between turbulence and advection on the diffusivity D. Secondly, we look in more detail at the mixing mechanisms responsible for mixing and buoyancy transport across a density interface. The density interfaces are very common in the natural environment. A typical example is the thermocline, which separates the upper mixed region of the ocean from the stratified ocean interior. In our experiments, in order to prevent homogenization, we stabilize the density interface by adding a source of fresh water and a source of dense water at the top and bottom of the tank respectively. Analogously to the prior set-up, we withdraw the same volume flux as the supply by two sinks, and wait for the steady state before measuring the density and velocity field and recording videos of the visible mixing phenomena. We find that the dominant mixing mechanism is localized at the interface and it is diffusive, as the time averaged correlation of density and vertical velocity fluctuations at the interface is a good approximation of the total vertical salt transport. We will also present the velocity and turbulence field, as well as the macro (integral) and micro (Taylor) length scales in the vertical, radial and azimuthal direction. The mixing mechanism in a two-layer fluid also involves a single wakelike perturbation that originates at the interface, close to the inner cylinder, and spreads out radially and azimuthally, with a peak period Tp \propto 1/\Omega, and a coeffcient of proportionality equal to 12\pi. From the shadowgraph images we infer that the mixing phenomenon, able to break the sharp gradients and to promote classical diffusion, is intermittent and lasts for approximately 40% of the peak period, causing the interface to fade away and letting parcels of intermediate density be vertically transported. Finally, we develop a model for the salt diffusivity based on diffusion inside the trailing edges of the wake.