In this study we simulate numerically the Reynolds' experiment for the tran
sition from laminar to turbulent flow in a pipe. We present a discussion of
the results from a dynamical systems perspective when a control parameter,
the Reynolds number, is increased. The Landau scenario, where the transiti
on is described by the excitation of infinite oscillatory modes within the
fluid, is not observed. Instead what happens is best explained by the Ruell
e-Takens scenario in terms of strange attractors. The Lyapunov exponent and
fractal dimension for the attractor are calculated together with a measure
of complex behaviour called the Lempel-Ziv complexity. (C) 2001 Elsevier S
cience B.V. All rights reserved.