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.