Fluid movement driven by a density difference is very common. When a freezer is opened, or a window on a winter's day (a ventilation flow), you may have noticed that the dense, cold air rushes across your feet. This effect can be felt even if you are on the other side of the room, the cold air warming a little as it mixes with the warmer air above, but remaining sufficiently cool and distinct as it flows like a flood across the floor.

These are part of a very broad family of fluid flows present across our homes, industries, and the wider environment, known as gravity-currents. Ventilation flows are important to understand for the spread of pathogens and disease, and cold-fronts are essentially the same but on the scale of 100-1000km. In industry, accidental spills of hazardous gas must be planned for, and suitable defences put in place. A very dangerous subset of gravity-currents are particle-driven currents, the suspended particle load providing the driving density and facilitating immense destructive power. For example, powder-snow avalanches are a hazard in mountainous regions, easily burying people and buildings. Pyroclastic density currents, searing hot clouds of ash released by volcanos and flowing out across the ground, famously buried Pompeii, leaving a city of people entombed in volcanic rock. Massive submarine turbidity-currents, >1000km long and moving at up to 10m/s, carry nutrients and carbon into the deep ocean, and have destroyed numerous cables and pipes carrying internet data or energy. Smaller (though still substantial) turbidity-currents will pose an increasing hazard to the UK as we develop deep-marine wind power, which must be connected back to shore by cables. The feasibility of these and other developments rely on our ability to predict and mitigate natural hazards.

The front the current pushes aside the ambient fluid, and it is the dynamics here which determine the rate of advance of the current. In addition, this region is a principal source of mixing, and for some currents it is also a region in which there is intense erosion of the bed. As the current mixes with the fluid around it, it becomes more dilute, and the current becomes bigger while simultaneously having a reduced driving density. Conversely, as it erodes the bed the driving density increases. Thus, the front exerts a very strong control on the advance of the current, and the mixing and erosional processes are a critical part of this. However, to date these processes have not been included in the mathematical models that are designed to predict these currents, which has limited their applicability to flows over short distances so that the mixing does not substantially affect on the overall density. Additionally, the front of the current is the most dangerous part: the same processes that enable the rapid erosion of the bed can facilitate immense destructive power.

In this fundamental scientific study, I will develop novel mathematical models that capture the dynamics of the front of a gravity-current, including the mixing and erosional processes. First, experimental work using newly developed techniques will yield data of unprecedented quality for a cool, temperature driven current, measuring the details of the vortices and mixing in both the head of the current and throughout. Additional experiments will focus on capturing the details of the erosional processes in sediment-driven currents. Informed by these measurements, I will capture the vital aspects of the dynamics of the head within a new mathematical model, for the first time including the mixing and erosional processes. Finally, the model of the head will be combined with a model for the rest of the current, which I developed previously, to give a complete model that can predict the motion of the current. This urgently required project represents a substantial leap-forward in our understanding and predictive power for this important and dangerous class of flows.