Centre manifold analysis of the Hasegawa-Wakatani equations.
Dr Linda Stals (Australian National University)
MSI Computational Maths SeminarDATE: 2010-09-20
TIME: 16:00:00 - 17:00:00
LOCATION: G35 John Dedman Building
CONTACT: JavaScript must be enabled to display this email address.
ABSTRACT:
We have written a code to model the Hasegawa-Wakatani equations. The output from the simulations is very complex, exhibiting both turbulence and long term trends. We have also found examples where instabilities appear. Are these instabilities a numerical artifact or a result of the properties of the equations? Are the simulations correct? Unfortunately the nonlinear terms in these equations are such that we cannot use the linear part of the system to predict the behaviour of the overall system. There is also currently not many reliable sources in the literature that we can use to compare our results against (I will mention in the talk why that is the case).
We have developed a centre manifold analysis of the Hasegawa-Wakatani equations. This analysis allows us to project down onto a small system that is relatively easy to study. These results in turn can be used to predict the behaviour of the original, large, full system.
Our analysis has highlighted some interesting properties of the equations that, as far as we are aware, have not been previously discussed.
We will present the centre manifold analysis in the talk and apply it to some example simulations.
BIO:
http://wwwmaths.anu.edu.au/~stals/
