Transition to turbulence in the Reynolds’ experiment

In this study we simulate numerically the Reynolds’ experiment for the transition 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 transition is described by the excitation of infinite oscillatory modes within the fluid, is not observed. Instead what happens is best explained by the Ruelle–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.