On analogies between turbulence in open flows and chaotic dynamical systems.

The authors briefly study turbulence in open flow systems in the context of concepts developed in studies of chaotic dynamical systems. Although several flows were examined, particular attention will be focussed on the question of transition to turbulence in coiled pipes; some degree of correspondence with the Ruelle-Takens-Newhouse route to chaos is indicated. Using the Grassberger-Procaccia algorithm, the dimension of the attractor for velocity signals during and immediately after transition to turbulence was computed. The results, such as they are, indicate that the dimension is relatively low. Brief comments will be made on the difficulties of computing the dimension, as well as on the relevance of strange-attractor theory to fully develop turbulence. (A)