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In this paper, we investigate steady inviscid compressible flows with radialsymmetry in an annulus. The major concerns are transonic flows with or withoutshocks. One of the main motivations is to elucidate the role played by theangular velocity in the structure of steady inviscid compressible flows. Wegive a complete classification of flow patterns in terms of boundary conditionsat the inner and outer circle. Due to the nonzero angular velocity, many newflow patterns will appear. There exists accelerating or decelerating smoothtransonic flows in an annulus satisfying one side boundary conditions at theinner or outer circle with all sonic points being nonexceptional andnoncharacteristically degenerate. More importantly, it is found that besidesthe well-known supersonic-subsonic shock in a divergent nozzle as in the casewithout angular velocity, there exists a supersonic-supersonic shock solution,where the downstream state may change smoothly from supersonic to subsonic.Furthermore, there exists a supersonic-sonic shock solution where the shockcircle and the sonic circle coincide, which is new and interesting.

Steady Compressible Radially Symmetric Flows with Nonzero Angular Velocity in an Annulus