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The study of fluid dynamics is concerned with understanding and modelling the flow of liquids, gases, and plasmas through their interaction or application of external forces.

Our research group concentrates on solving problems in which the evolution of a fluid configuration is to be determined after some initial condition or disturbance is applied. Configurations of interest to us lend themselves to analytical and semi-analytical solution techniques.

When a light (less dense) fluid lies below a heavy one, the situation is unstable because the two fluids try to interchange positions. This situation occurs reasonably often in nature; painting a ceiling is an example of this (the paint is heavier than the air below it!), and another such example occurs in the ocean, with certain flows under ice sheets. Any interface between the two fluids is therefore unstable, and a small disturbance to the interface will grow with time (the paint on the ceiling can drip). These types of flows are called Rayleigh-Taylor instabilities.

We are studying various types of Rayleigh-Taylor type flows caused by heating and electromagnetic interaction. We are also working on situations in which a lighter fluid is injected into a heavier one. These are believed to play a role in astrophysics, and can involve circular (in two dimensions) or spherical (in three dimensions) bubbles of light fluid that grow with time. Various types of jets and over-turning plumes can be formed.

*Figure1: Outflow from a line source in a fluid.*

Convection is induced in a layer of compressible fluid by heating and cooling different parts of the lower wall. As the amplitude of this modulated temperature is increased the behaviour of the flow may become highly non-linear or even unstable. This work has application to meteorology as well as to various industrial problems.

Normally, a high or low-pressure region in meteorology occurs as a roughly circular system across the Earth's surface, when viewed from above (by satellite). This is a result of the Coriolis acceleration due to the Earth's rotation. However, it is sometimes observed that these circular systems can develop wave-like instabilities at their edges. These waves appear to grow with time, and occasionally produce large-amplitude finger-like structures at the edge of the high or low pressure system.

It is known, in other circumstances, that a system of fluids moving with different speeds either side of an interface is an unstable situation. The shear at the interface causes waves to grow in time. This is the famous Kelvin-Helmholtz instability, and has been the subject of much study. Recently, methods developed at the University of Tasmania have been used to study these unstable waves in the difficult case when they become of large amplitude, and complex non-linear effects become important.

In this project, these methods will be used to study the growth of unstable Kelvin-Helmholtz type waves on the edge of rotating high or low pressure systems in meteorology. The equations for a thin atmosphere will be used, and if possible, these may be approximated by f-plane or beta-plane equations, as is common in meteorological modelling. In any case, the solution for a circular high or low pressure system will be subjected to a perturbation at its edge, and the growth of these waves in time will then be studied.

- Professor Larry Forbes
- Professor Graeme Hocking, Murdoch University
- Dr Tim Stokes, The University of Waikato
- Jason Cosgrove PhD student
- David Horsley PhD student

*Figure2: Convection by temperature modulation on the lower wall.*

Authorised by the Head of School, Physical Sciences

2 May, 2018

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