  We consider a diffusion model with limit cycle reaction functions, in the
presence of convection. We select a set of functions derived from a realistic
reaction model: the Schnakenberg equations. This resultant form is
unsymmetrical. We find a transformation which maps the irregular equations into
model form. Next we transform the dependent variables into polar form. From
here, a travelling wave analysis is performed on the radial variable. Results
are complex, but we make some simple estimates.
  We carry out numerical experiments to test our analysis. An initial `knock'
starts the propagation of pattern. The speed of the travelling wave is not
quite as expected. We investigate further. The system demonstrates distinctly
different behaviour to the left and the right. We explain how this phenomenon
occurs by examining the underlying behaviour.
