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Layering in Fluid Dynamical Systems

Academic lead
Prof David Hughes, School of Mathematics
Dr Stephen Griffiths, School of Mathematics, Prof Peter Jimack, School of Computing
Project themes
Geophysical flows

One of the most interesting features of fluid dynamical systems is their tendency to form layers or “staircases”. These are particularly apparent, as density staircases, in double-diffusive systems in which two competing elements contribute to the density and, crucially, diffuse at different rates. The most studied example is the heat-salt system in the oceans (so-called thermohaline convection); double diffusive convection is also believed to be of importance in stellar cores, where the competing elements are heat and a compositional gradient. Another, ostensibly very different, system that produces layering is rotating turbulence (e.g. beta-plane turbulence) in which a staircase in potential vorticity is formed, manifested by strong jets.

This project will explore, through simple models, the entire nature of staircase formation – the physical ingredients necessary for their formation, the scale at which they initially form, and how subsequent staircase mergers occur. Of course, there has been considerable interesting work in this area. Chiefly though this has been through what are known as mean field models which, by their very nature, are unable to address, for example, the initial stages of staircase formation. Thus quite fundamental problems remain unanswered. The project will analyse various models of fluid turbulence – concentrating manly on double-diffusive convection – to address some of these issues through a combination of theoretical and numerical approaches.