TRANSIENT GROWTH IN CIRCULAR PIPE-FLOW .1. LINEAR DISTURBANCES

The behavior of very low-amplitude disturbances in a circular pipe is considered. Direct simulation of the Navier-Stokes equations is used t o compute the evolution of two- and three-dimensional waves and the re sults are found to be in good agreement with solutions to the Orr-Somm erfeld 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 wavelengt h exhibits a very rich structure of temporal evolution depending on th e particular initial condition chosen. Comparison with recent results reported by Bergstrom on optimal disturbances is also given. In Part I I of this study these findings will be extended to the nonlinear devel opment of like disturbances.