The stability of Poiseuille flow in a pipe of circular cross-section

Abstract

The stability of Poiseuille flow in a pipe of circular cross-section to azimuthally varying as well as axisymmetric disturbances has been studied. The perturbation velocity and pressure were expanded in a complete set of orthonormal functions which satisfy the boundary conditions. Truncating the expansion yielded a matrix differential equation for the time dependence of the expansion coefficients. The stability characteristics were determined from the eigenvalues of the matrix, which were calculated numerically. Calculations were carried out for the azimuthal wavenumbers n = 0,…, 5, axial wavenumbers α between 0·1 and 10·0 and α R [les ] 50000, R being the Reynolds number. Our results show that pipe flow is stable to infinitesimal disturbances for all values of α, R and n in these ranges.