A note on shocks in nonlinear similarity fields

The authors derive a necessary and sufficient condition for the existence of similarity shocks for a system of two quasi-linear, first-order partial differential equations. These shocks, expressed as lines of discontinuity in the dependent variables across which appropriate jump conditions must be satisfied, comply with the similarity assumption and occur along similarity lines across which the correct jump conditions will be expressible in terms of similarity variables only. A procedure for deriving similarity shocks is applied to the small perturbation equation of two-dimensional Cartesian and axisymmetric transonic flow.