An analytic approach for calculating absolutely unstable inviscid modes of the boundary layer on a rotating disk

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Abstract

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.

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Turkyilmazoglu, M., & Gajjar, J. S. B. (2001). An analytic approach for calculating absolutely unstable inviscid modes of the boundary layer on a rotating disk. Studies in Applied Mathematics, 106(4), 419–435. https://doi.org/10.1111/1467-9590.00173

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