Dispersion equations in the problem of the stability of transonic flows and some of their properties

For the Navier-Stokes equations, asymptotic simplifying techniques are discussed aimed at the description of unsteady boundary-layer processes associated with the formation of instability. The form of the asymptotic series is based on the triple-deck treatment of solutions to boundary value problems (viscous-inviscid interaction). Although most attention is focused on transonic outer flows, a comparative analysis with the asymptotic theory of boundary layer stability in subsonic flows is given. The parameters of internal waves near the lower and upper branches of the neutral curve are associated with different structures of the perturbation field. These parameters satisfy dispersion relations derived by solving eigenvalue problems. The dispersion relations are investigated in complex planes.