A spectral Petrov-Galerkin formulation for pipe flow I: Linear stability and transient growth

Abstract

A spectral Petrov-Galerkin scheme for the numerical approximation of flow in a circular pipe is presented. The mathematical formulation is presented in detail focusing on the analyticity of solenoidal vector fields used for the approximation of the flow. A comprehensive study of linear stability is reported for axisymmetric, non-axisymmetric, streamwise dependent and streamwise independent perturbations . The scheme provides spectral accuracy in all cases studied and the numerical results are in agreement with former works. A parametric exploration of pseudospectra and transient growth has been carried out for the aforementioned cases.

This research was supported by UK Engineering and Physical Sciences Research Council Grant GR/M30890.