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An Analytic Approach for Calculating Absolutely Unstable Inviscid Modes of the Boundary Layer on a Rotating Disk

An analytical treatment of inviscidly absolutely unstable modes is pursued using the long‐wavelength asymptotic approach. It is shown using the inviscid Rayleigh scalings in conjunction with the linear critical layer theory that the rotating‐disk boundary layer flow undergoes a region of absolute instability for some small azimuthal wave numbers. The analytically calculated branch points for the absolute instability are found to be in good agreement with those obtained via a numerical solution of the inviscid Rayleigh equation.