Dr Duncan Farrow

Room: S&C/3.004

Research

Environmental and industrial modelling; free-surface hydrodynamics.

Projects

Hydrodynamic Stability

When a body of water (such as a lake) is cooled from above, the surface water becomes more dense than the deeper water. If the cooling is sufficiently strong, this leads to an unstable configuration - the water column is prone to overturning, leading to Rayleigh-Bernard convection. Depending upon the situation, this can be considered as either good or bad. The above scenario is one example from the study of hydrodynamic stability where there is typically two competing influences (one stabilising and one destabilising). This project will look at the background to this phenomenon and consider the effect of other influences on the stability. For example, there may be some internal heating, an existing temperature structure or a background velocity shear. There is scope in this project for a significant computational component.

Natural Convection in the Environment

Natural convection is the flow of fluid with variable density under the influence of gravity. The atmosphere and the oceans provide many examples of such flows where the density variability can be due to temperature changes (due to the sun), salinity or pressure. This project will consider some idealised mathematical models of these types of systems with a particular emphasis on natural convection in lakes and reservoirs.

Wave Profiles Behind Ships

As a ship travels over the water it leaves behind a wave field. This wave field contains energy which the ship must provide. This is felt by the ship as 'wave drag'. The wave drag on a given ship depends on the speed of the ship and, interestingly, its geometry. This project considers this problem, and, in particular, looks at whether or not the wave drag on a ship can be reduced by modifying its geometry in some way. The study of this problem involves use of a number of classical methods of applied mathematics as well as providing scope for a computational component.

There are a number of suitable projects available in mechanics, fluid mechanics or biological or chemical systems, including flow of air in the lungs, or blood through arteries, modelling temperature and density in a reservoir, withdrawing water from density-stratified fluids, modelling wave heights in a harbour, and flow of water or oil underground.

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