Thermal Convection and Buoyancy Driven Flows

Hot fluid approaching a cool wall at the left side of a wide channel, streamlines and isotherms.

Many fluid flows are driven by buoyancy, the tendency of hot fluid to be less dense and therefore rise, and cold fluid to sink. Prime examples of this are found in planetary atmospheres. Unequal heating of the Earth's surface by the Sun leads to a large-scale circulation in the atmosphere which transports heat form equatorial regions to the poles. This motion is also influenced by the rotation of the Earth. The resulting large-scale flow is prone to instability, leading to the complex flow patterns and pressure distributions typically observed in weather maps. Likewise, buoyancy is primarily responsible for the large-scale motion of the oceans and, on a smaller scale, the dynamics of lakes and reservoirs. It is also relevant in the very large-scale motions taking place within the Earth's crust, which are described by the theory of plate tectonics and result in the slow movement of the continents and the existence of earthquakes and volcanoes.

Buoyancy-driven flows are important in a variety of technological applications ranging from the cooling of nuclear reactors and electronic components in computers to crystal growth, double glazing and the spread of pollutants through groundwater.

Research carried out within the Mathematics Department is aimed at using simple theoretical models to understand both the main features of thermally-driven flows and their stability properties. Numerical and asymptotic methods are used to solve the relevant governing equations and where possible results are compared with experimental data and field measurements. Results gained by the theoretical approach often provide new and significant insight which can be used to help understand the complex motions observed in both technological and geophysical applications and to help predict, for example, future changes in the Earth's climate.