Singularity induced bifurcations in multiple transonic crossings of unsteady self-similar gravitational flows

A singularity induced bifurcation (SIB) phenomenon is used in this paper to analyze transonic flow in an unsteady gravitational field. Multiple sonic crossings by a single trajectory in the gravitational field are characterized by the divergence of eigenvalues of the linearized model, folded saddles and nodes, as well as the existence of impasse points at the sonic manifold. The analysis is done in the framework of self-similarity shockless solutions. Two particular implicit ODE models of the transonic flows in the gravitational field around a central point mass are analyzed.