Oscillatory wakes occur in a wide range of reaction-diffusion systems, consisting of either periodic travelling waves or irregular spatiotemporal oscillations, behind a moving transition front. In this paper, the use of a finite boundary moving with an imposed speed to mimic the transition front is considered. For both lambda-omega systems and standard predator-prey models, the solutions behind these moving boundaries agree very closely with the behaviour behind transition fronts, provided suitable end conditions are used on the moving boundary. This confirms that the transition front can be regarded as determining the solution, by forcing a particular periodic wave at the boundary of the wake region. In the case of lambda-omega systems, a detailed numerical study of solutions on a fixed-length finite domain with a periodic wave solution forced at the boundaries is performed As the domain length is varied as a parameter, the long-term temporal behaviour undergoes bifurcation sequences that are well known as routes to chaos in ordinary differential equations. This suggests that irregular wakes actually have the form of a perpetual transient in a progression towards chaos. Finally, the way in which the moving boundary results can be used to design an experimental verification of the oscillatory wakes phenomenon in a chemical system is discussed.