Multimode instability of the three-dimensional boundary layer along an infinite attachment line

Linear stability of a similar boundary-layer flow to oblique-wave disturbances is governed by partial differential equations with respect to nondimensional vertical coordinate and the chordwise Reynolds number R-1. In the case of swept Hiemenz flow, the equations admit a series solution expanded into inverse powers of R-1(z) and are then decomposed into an infinite sequence of ordinary differential systems with the leading one posing an eigenvalue problem to determine the first approximation to the complex dispersion relation. Numerical estimation of the series solution indicates a much lower critical Reynolds number of the oblique-wave instability than R-e=583 of the spanwise-traveling T-S instability.