The inviscid instability of a Blasius boundary layer at large values of the Mach number

The unstable and neutral modes of a compressible boundary-layer flow past an insulated flat plate are discussed in the limit of infinite Mach number. These modes have been documented by Mack and many of the asymptotic results derived here are becoming evident in his computations at finite values of the Mach number. Of particular interest is the existence of a vorticity mode for which the wavenumber is a discontinuous function of Mach number at finite Mach number but is continuous in the limit M ∞ → ∞. At large Mach number this is the most unstable mode, and is expected to have relevance also in the hypersonic limit when the flow field is no longer shock-free.