## Dr. Sean Oughton: Research Interests

My current research interests centre on understanding the behaviour of turbulent flows. Physically we all have a good understanding of what a turbulent flow is. For example, white water rapids are clearly turbulent, whereas a (stationary) jar of honey is not. In fact, on the earth most flows, at most times, are turbulent.

[Mathematically, one might say that a turbulent flow is characterised by motions which occur over a broad range of length (and time) scales and that these motions interact nonlinearly. It is this nonlinear nature of the problem which makes it simultaneously so rich and so challenging. ]

A particular interest is magnetofluid turbulence, where the fluid is electrically conducting so that one must consider not just the behaviour of the fluid's velocity, but also that of its magnetic field. Examples of magnetofluids include liquid metals (e.g. mercury) and plasmas (e.g. the sun, the solar wind, the working fluid in nuclear fusion devices). Most of the matter in the universe is thought to be in the plasma state, that is, the atoms have been ionised.

One way to study conducting fluids is using magnetohydrodynamics (MHD). This is the marriage of the equations of fluid dynamics with those of electrodynamics, and provides a good approximation to the behaviour of various parts of the solar system (or heliosphere). Important dynamical features of MHD include waves, turbulence, plasma heating, and particle acceleration.

The work involves a mixture of theory (including statistical mechanics and modeling) and computer simulations of the governing equations.

## 2D MHD Movies:

Two (mpeg) movies of decaying two-dimensional MHD turbulence (with Reynolds numbers of 800) are available:
Vorticity movie (vorticity is a measure of the local rate of rotation of the plasma).
Electric current density movie.

Note how vortices with the same sense of rotation tend to ``collide'' and merge, leading to a smoothing of the vorticity. The merger process often involves a larger vortex shredding a smaller one which is wrapped around the larger one and eventually absorbed into it. In the current density movie the dominant structures are seen to be much more sheet-like than in the case of the vorticity. In the heliosphere, similar (but more intense) ``current sheets'' are sites where particles are accelerated to relativistic energies and intense heating of the plasma can occur.

## 2D Navier-Stokes Movies:

You can also see some sample images from an investigation of the evolution of a (non-conducting) turbulent flow. These are surface plots of the vorticity (curl of the velocity) from a 512^2 simulation of the two-dimensional hydrodynamics (Navier-Stokes) equations. The initial conditions are turbulent and the merging of like-sign vortices is evident. [See the publications list, references 1, 2, and 4.] Each plot is the vorticity at a different time. Time increases from left to right.

There are also a couple of movies of this for the earlier times and for the later times.

[Vorticity is a measure of the ``swirliness'' of a flow. A vortex, such as the one over the plughole in an emptying bath, has lots of vorticity, whereas the water flowing straight out of a tap or a hose doesn't have so much. ]

This particular simulation took about 400 cpu-hours to complete on one of the fastest supercomputers available at the time (in the late 1980s). Today it could be done on a standard PC in well under a week!