James Reilly

Project Title: New Horizons in Low-Order Modelling of Fluid Flows

The study of fluid dynamics underpins a bewildering variety of fundamental scientific problems which arise from a wide range of practical applications, including geophysical flows of mud and lava, microfluidics, weather forecasting and computer graphics.

The motion of many different fluids is well-described by the famous Navier-Stokes equations (and their many generalisations). However, while these can, in principle, be solved numerically, the computational cost can be very high. An alternative option is to examine the equations analytically. While they cannot, in general, be solved exactly, a very successful approach has been to make certain well-justified simplifying assumptions to reduce the dimensionality of the equations to produce appropriate low-order models. Such models retain the essential physics inherent in the original equations, but may be analysed analytically and/or numerically much more readily. The most commonly used assumption is that the flow varies much more rapidly in one direction than in another (i.e. the flow is “thin”).
However, this model automatically excludes innumerable industrially-important flows as well as many flows of theoretical importance.

However, recent work indicates that the same general methodology can also be applied to flows outwith this assumption, potentially opening the door to understanding a wide range previously intractable flows.