Transient growth in circular pipe flow. I. Linear disturbances

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Abstract
The behavior of very low-amplitude disturbances in a circular pipe is considered. Direct simulation of the Navier–Stokes equations is used to compute the evolution of two- and three-dimensional waves and the results are found to be in good agreement with solutions to the Orr–Sommerfeld equation for Hagen–Poiseuille flow. Transient growth mechanisms are also investigated computationally, in which case it is found that the growth of disturbances with large but finite streamwise wavelength exhibits a very rich structure of temporal evolution depending on the particular initial condition chosen. Comparison with recent results reported by Bergström on optimal disturbances is also given. In Part II of this study these findings will be extended to the nonlinear development of like disturbances.