Spectral calculations of the spatial stability of non-parallel boundary layers

The linear spatial stability of the Blasius boundary layer is considered. The semi-infinite domain is transformed to a finite domain for calculation. The solution is then obtained by expansion in Chebyshev polynomials. This results in a nonlinear (in the parameter) eigenvalue problem. In the first part of the paper, the eigenvalue spectrum is computed using the parallel flow approximation. The neutral stability curve and eigenfunctions are also found. In the second part, the first-order effects of boundary layer growth are included. The method of multiple scales is used and the method of solution uses a matrix approach. The advantages of this method are discussed and some calculations of nonparallel flow effects are included.