Spectral Tau Formulation for Cylindrical Flows with Strong Angular Momentum Gradients and Centrifugal Instability Analysis

This repository accompanies the manuscript: “Spectral Tau Formulation for Cylindrical Flows with Strong Angular Momentum Gradients and Centrifugal Instability Analysis.” It documents a product-consistent spectral Tau formulation designed to neutralize singular cylindrical operators of the form 1/rn1/r^n1/rn in linear stability problems. The method analytically absorbs singular coefficients into a structured polynomial basis, preventing pointwise evaluation of inverse radial terms and significantly improving conditioning relative to Chebyshev collocation discretizations. The archive includes: • Spectral convergence data• Conditioning comparison tables• Eigenvalue growth-rate datasets• Radial eigenmode profiles• Implementation notes This repository supports reproducibility and further development of high-order spectral methods in cylindrical geometries.