Box models of thermohaline circulation

This thesis investigates a number of buoyancy-driven flows in stratified environments that are motivated by the thermohaline circulation of the ocean. Simple models are presented which reduce the dynamics to a few leading order processes and we present an intuitive investigation with simple experiments or numerical calculations. We study the fluid dynamics of locally intensified mixing, referred to as `boundary mixing' within the ocean literature, and also the effect of mixing between the up and downwelling flows on the steady and transient circulation within an idealised filling-box flow. In chapters 2 and 3 we present an experimental and theoretical study of boundary mixing. We investigate the transport of buoyancy and tracer through a closed basin with buoyancy fluxes supplied at the top and bottom boundaries and, in both chapters, we compare the two cases in which the mixing either occurs uniformly across the tank or is locally confined to one portion. In chapter 2 we establish the simplest case in which the buoyancy fluxes supplied at the boundaries lead to no net flow in the system. By tracking the movement of dye we are able to visualise the flow patterns. An analytical model is developed that is consistent with the vertical and lateral flows in the experiment as well as with the evolution of the salinity stratification. We investigate the interaction of this effect with a vertical buoyancy flux and a net vertical flow with boundary mixing in chapter 3. We examine the stratification and the flow that develops in the steady state case. Next we investigate the transient adjustment of the buoyancy stratification due to changes in the supplied buoyancy fluxes. In chapters 4 and 5 we shift the focus to filling-box flows and investigate the interior stratification that develops from a local finite-mass source of destabilising buoyancy and a distributed stabilising buoyancy flux, both supplied to the surface of the domain with the addition of interior diffusive mixing. In chapter 4 we present a model showing that the system is controlled by two key non-dimensional parameters relating the source volume flux to the volume flux of entrained fluid and to the diffusive flux, resulting in four distinct regimes. If this system is perturbed, it exhibits inertia in adjusting to the new equilibrium when the perturbation timescale is short compared to the adjustment timescale and is no longer representative of the quasi-steady state. However, these profiles are still consistent with the simplified `Abyssal Recipes' profiles which are controlled only by mass conservation with constant upwelling and diffusivity. In chapter 5 we present a similar box model in which the entrainment increases linearly with depth and investigate the inverted values for the diffusivity and the upwelling rate. This leads to the recognition that it is difficult to distinguish more complicated models from the simplified models just from the data. This thesis finishes with a summary and discussion of the results in chapter 6.