In this paper the methods of Parts 1 and 2 are extended to the case when the elliptic cylinder is executing angular oscillations about its centreline. At large distances from the cylinder the solution for a beam of waves tends to a similarity solution that decays more rapidly with distance than does the similarity solution for rectilinear oscillations described in Thomas & Stevenson (1972). Figure 4 shows in a remarkable way how the predicted wave profiles change with distance from the inviscid solution to the similarity one.

In the latter part of the paper the predictions of Parts 1 and 2 and other theories are compared with recent experimental observations. The results of the experiments are in good agreement with the predictions of Parts 1 and 2.