Temporal eigenvalue spectrum of the Orr–Sommerfeld equation for the Blasius boundary layer

A search for the eigenvalue spectrum of the Orr–Sommerfeld equation for the Blasius boundary layer is conducted. The investigation is numerical involving two different numerical methods. The resulting spectrum is found to depend on the finite interval of integration chosen for the numerical scheme. This spectrum is shown to be infinite and discrete whenever it is identified with the aid of numerical integrations. The spectrum belonging to the exact semi-infinite problem is inferred from the asymptotic behavior of the same spectrum. This is shown to be comprised of a finite discrete set and a continuous portion.