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

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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 wavenumbersn= 0,…, 5, axial wavenumbers α between 0·1 and 10·0 and αR[les ] 50000,Rbeing the Reynolds number. Our results show that pipe flow is stable to infinitesimal disturbances for all values of α,Randnin these ranges.

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