Many fluid flows in natural systems are highly complex, with an often beguilingly intricate and confusing detailed structure. Yet, as with many systems, a good deal of insight can be gained by testing the consequences of simple mathematical models that capture the essential physics. We’ll tour two such problems. In the summer melt seasons in Greenland, lakes form on the surface of the ice which have been observed to rapidly drain. The propagation of the meltwater in the subsurface couples the elastic deformation of the ice and, crucially, the flow of water within the deformable subglacial till. In this case the poroelastic deformation of the till plays a subtle, but crucial, role in routing the surface meltwater which spreads indefinitely, and has implications for how we think about large-scale motion in groundwater aquifers or geological carbon storage. In contrast, when magma erupts onto the Earth’s surface it flows before rapidly cooling and crystallising. Using analogies from the kitchen we construct, and experimentally test, a simple model of what sets the ultimate extent of magmatic intrusions on Earth and, as it turns out, on Venus. The results are delicious! In both these cases, we see how a simplified mathematical analysis provides insight into large scale phenomena.
- Industrial and Applied Mathematics Seminar