FLOQUET STABILTY OF TIME PERIODIC PIPE FLOW

Jonathan Nebauer, Hugh Blackburn
unpublished
A Chebyshev spectral co-location and divergence-free method is adapted to solve the linearised Navier-Stokes (LNS) equations for time-periodic pipe flow. The method is spectral in the pipe axis and azimuth, allowing for specific axial and azimuthal wave numbers. A Krylov subspace method is used to find the leading (real-part) eigenvalues of the LNS flow evolution over one oscillation period. We demonstrate the relevance to Floquet Theory and proceed to assess the linear-stability of these
more » ... lity of these flows. The outcomes are compared against known linear stability results in pipe flows. Finally, an apparent discontinuity in the eigenproblem is investigated and explained by its physical and numerical relevance. This investigation lays the groundwork for a validation study of recently presented three-dimensional linear instabilities in periodic pipe flow.
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