Linearized pipe flow to Reynolds number $10^7$

Abstract

A Fourier-Chebyshev Petrov-Galerkin spectral method is described for high-accuracy computation of linearized dynamics for flow in an infinite circular pipe. Our code is unusual in being based on solenoidal velocity variables and in being written in MATLAB. Systematic studies are presented of the dependence of eigenvalues, transient growth factors, and other quantities on the axial and azimuthal wave numbers and the Reynolds number R for R ranging from $10^2$ to the idealized (physically unrealizable) value $10^7$. Implications for transition to turbulence are considered in the light of recent theoretical results of S. J. Chapman