Transonic laminar interacting boundary layers in narrow channels

The investigation of transonic viscous-inviscid interactions is hampered by the fact that the nonlinear small disturbance equation which governs the e xternal flow has to be solved simultaneously with the nonlinear boundary la yer equations. This poses an extremely difficult numerical problem which ha s been treated so far with limited success only. However, if the medium is confined in a sufficiently narrow channel, the pow outside the viscous wall layers is one-dimensional in the leading order approximation which in turn allows the derivation of a solution in closed form. This significantly sim plifies the construction of numerical solutions which nevertheless display essential features of transonic flows associated with the transition from s ubsonic to supersonic conditions or/and vice versa.