THE STABILITY OF SMOOTH TWO-DIMENSIONAL TRANSONIC FLOWS

The stability of smooth (shock-free) two-dimensional transonic flows to acoustic disturbances is discussed. The problem is considered in the context of transonic flow over airfoil sections, with weak waves moving upstream into the region of embedded supersonic flow. In particular, Spee's work on stability criteria for such flows is reviewed, and the problem is reformulated within the framework of geometrical acoustics. It is shown that the assumptions appropriate for a linearized theory appear to fail when acoustic waves become tangent to characteristics of the undisturbed flow field. The assumptions of linear theory are implicit in Spee's work. The results presented here indicate that stability theory must be based on a more careful and detailed analysis of wave propagation through the supersonic region. (Author)