An axisymmetric viscous-transonic equation is presented. A nozzle type similarity solution of this equation has been found, which describes the initial stages in the development of shock-waves downstream of a converging-diverging nozzle throat. This solution is an extension of a two dimensional solution found previously (Sichel 1966). By an appropriate choice of an arbitrary scaling constant solutions were found such that there is essentially a veak normal shock near the axis with effects of wall and shock wave curvature occurring only at a sufficiently large radius. The upstream and downstream asymptotic behavior of these viscous-transonic nozzle solutions has been investigated. in ACKNOWLEDGMENT The authors would like to express their appreciation to the Army Research Organization in Durham, N. C. for their support of this work under Contract | DA-31-124-ARO-D-276. ■ The contents of this report have been submitted to the Journal of Fluid Mechanics for publication.

Similarity solutions of the viscous transonic equation describing source and source vortex Ilows have been found. These solutions contain shock-like transitions from the supersonic to the subsonic branch of the corresponding inviscid solutions, while the singularity near the sonic point of the inviscid solutions is shifted to a smaller radius. It is shown that this similarity solu±ion is identical to the transonic viscous compressible source and sink flow solutions of Wu (1955) and Sakurai (1958).

The equations for the plane viscous transonic flow of a relaxing gas are derived for free stream velocities near the equilibrium and frozen speeds of sound. One‐dimensional solutions are found which show the influence of the compressive viscosity upon the structure of a compression wave in a relaxing gas. The viscous structure of the corner region or acceleration wave which occurs when the upstream velocity just equals the frozen speed of sound is investigated in detail. The structure of a partially dispersed wave including the transition from the upstream viscous shock to the downstream relaxation zone is also determined.