  The Hasegawa-Wakatani models are used in the study of confinement of hot
plasmas with externally imposed magnetic fields. The nonlinear terms in the
Hasegawa-Wakatani models complicate the analysis of the system as they
propagate local changes across the entire system. Centre manifold analysis
allows us to project down onto much smaller systems that are more easily
analysed. Qualitative information about the behaviour of the reduced system,
such as whether it is stable or unstable, can be used to predict the behaviour
of the original full system. We show how the simple structure of the linear
part of the Hasegawa-Wakatani equations can be used to define these projection
operators. The centre manifold analysis will be used on a few examples to
highlight certain properties of the Hasegawa-Wakatani models.
