Abstract
Through-flow theory and cascade flow theory are well known techniques used as efficient tools in order to build approximations to the actual flow in an axial turbomachine. Here we use a technique of matched asymptotic expansions in order to glue together these two kinds of approximations. Throughflow theory forms the basis for the outer expansion while cancade theory forms the basis for the inner one: matching provides boundary conditions for both flows. It appears that for the downstream throughflow, a technique of multiple scales is necessary, in the vibrating case, in order to deal with the unsteady wakes, generated by the vibrating blades, and slowly modulated, downstream by the steady part of the throughflow.
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