Final Activity Report Summary - STRATMIX_CPCAULFIELD (Rigorous bounds on mixing in stratified shear flows: A route to improved parameterizations) The transfer of heat and momentum by fluid motions is a key process in the atmosphere and the oceans. Understanding the mechanisms by which heat is transferred is essential to our description of the global climate system. Improvements in the predictive power of models which attempt to simulate the behaviour of the climate system years into the future will rely on greater certainty in the representation of this heat transfer. The global climate system evolves on a huge range of spatial and temporal scales. However, it is becoming increasingly well-appreciated that a key component of the behaviour of the entire system is relatively small-scale motions associated, for example with tides, breaking waves, and boundary effects. Due to their small scales, such processes inevitably have to be parameterized within large models. One of the most important and significant small-scale processes is stratified mixing driven by turbulence, i.e. the irreversible mixing of fluid of varying densities by small-scale processes. This has a definite energetic implication, as mixing of fluid of varying density changes the potential energy of the system in a non-trivial way, while also changing the kinetic energy of the system due to viscous dissipation. The relative size of these two energy conversions (i.e. the mixing efficiency) is a key component of any appropriate model of mixing within a stratified fluid, such as of course the atmosphere and ocean. There has been much previous work on this problem, and this project has aimed to add to the understanding of this problem by using a combination of rigorous mathematical tools, numerical simulation and laboratory experiments to aid in the development and testing of improved parameterizations. In particular, the project has used mathematical techniques to generate rigorous bounds on the amount of mixing which can occur within a model problem. The characteristics of the mixing, in particular its efficiency was determined by a novel mathematical approach. Furthermore, two experimental studies, using a novel technique, added substantially to the understanding of mixing within stratified flows. The experimental technique used careful lighting and dye techniques to measure in a time-dependent manner the mixing within a range of relevant model flows, identifying both the critical importance of initial conditions and the possibility of exceptionally and surprisingly efficient mixing under certain, realistic conditions. Finally, the project investigated numerically stratified mixing processes on a very small scale. Interestingly, this demonstrated a mechanism by which the very presence of the stratification can trigger a flow instability (and hence mixing) in circumstances where a homogeneous flow would be completely stable. This suggests a whole new avenue of research into the ways that density variations and flow can interact to redistribute mass and energy within a flow.