A theoretical study is made of the conditions for existence of the three-dimensional, or partial-span patterns of rotating stall of the axial flow com¬pressor within the framework of small perturbation theory. Two specific prob¬lems are considered. For the infinite two-dimensional cascade, it is shown that a spanwise variation of lift perturbation is impossible; i.e., a rotating stall pattern must be aligned with the blades rather than in any skew direc¬tion. Second, it is shown by a similar method that no disturbance of lift can propagate relative to the blade elements of an axially-symmetric compressor stage which, in terms of mean flow, produces a free vortex-swirl distribution. These two negative results suggest the value of further research into the geo¬metrical conditions necessary for the existence of three-dimensional propagat¬ing stall.nFor the case of vortex swirl (and also the infinite cascade) a full-span disturbance, having arbitrary amplitude, and traveling with the blade elements, is found to be possible, provided the applicable steady lift curve for all blade elements is a hysteresis loop.nBeing the last of a series of papers forming the final report of a study of the basic mechanisms of rotating stall, this report includes a discussion of the directions in which such research might reasonably proceed in the future.
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