An inviscid model, originally proposed by Bryson to describe the formation of laterally-symmetric vortices above bodies of revolution at large angles of incidence, is extended to describe flows without lateral symmetry. Each vortex is represented by a single line-vortex and conditions of cross-flow stagnation are applied at the postulated separation lines. The transverse component of the force acting on each vortex is balanced by an equal and opposite force acting on the cut connecting it to the adjacent separation line. It is shown that this model allows asymmetrical vortices to form in the flow over slender circular cones even when the separation lines are disposed symmetrically.

A complete unsteady Newton-Busemann flow theory, including centrifugal force corrections, was recently given by Hui and Tobak and successfully applied to study the dynamical stability of oscillating aerofoils (Part I) and bodies of revolution (Part II). The present paper extends these results, which are restricted to the first order in frequency, to general frequencies that may be applicable to flutter analysis as well. Furthermore, the new results are used to investigate the behaviour of the indicial response functions in unsteady flow at very high Mach numbers. In particular, it is found that for a family of body shapes in the Newtonian flow, including the cone, the wedge, the delta wing and slender aerofoils, the aerodynamic response to a step change in angle of attack or pitching velocity contains an impulse at the initial instant. This is followed by a rapid adjustment to the new steady-flow conditions, the adjustment time being equal to that required for a fluid particle to travel a distance of the body length. The impulse component appearing at the infinite Mach number limit (Newtonian flow) is in effect an apparent mass term, analogous to that which occurs initially in the aerodynamic indicial response at the zero Mach number limit (incompressible flow). In the latter case the initial impulse is followed by an asymptotic adjustment to the new steady-flow conditions, theoretically taking infinite time, in direct contrast to the rapid adjustment in Newtonian flow.

The unsteady breakdown or stall of streamlined flow near the rounded leading edge of an aerofoil, as the small angle of attack is raised above its critical stall value, is studied theoretically for large Reynolds number motion. The unsteady developments take place first over a relatively slow time scale but then the corresponding solution breaks down with a singularity, forcing a switch to a faster and more nonlinear process. The latter involves a very pronounced local bulge appearing in the flow displacement, accompanied by reversed flow at the aerofoil surface, and comparisons with experimental observations of dynamic stall are noted.