One way to look at this is that you have a certain geometry (e.g. dia of each section, the blade spacing etc.) and a certain set of boundary conditions (e.g. far away from the system the P & T must return to ambient + continuum changes in P / T / flow etc. + velocity at wall set to zero) and a combustion zone with a specific mass contribution per unit time.
The pressure distribution and local flow profile is what evolves when you solve the governing flow and conservation equations. With the additional constraints offered by gas laws, commpressibility equations, heat transfer equations etc.
Sure, with the right (wrong?) set of parameters you can indeed "expand in both directions".
My point is, perhaps the analogy or the easy to understand qualitative explanation only takes you so far. At some point the flow direction is what evolves from solving a particular geometry with a particular set of boundary conditions.