Chaotic dynamics in open flow: The excited jet.

Abstract

We present a dynamical system analysis of an experimental study on an axisymmetrical excited air jet. The transition to turbulence---weak turbulence--- is investigated by imposing on the laminar flow a controlled excitation which triggers the spatial development of the jet instability. By longitudinal and azimuthal coherence and phase measurements, we find that a helical structure with azimuthal mode m=\ifmmode\pm\else\textpm\fi{}1 is being selected, in accordance with spatial linear stability analysis. Further downstream, the transition to turbulence is evidenced, through a decrease in spatial coherence, by destabilization and a breakdown of the helical structure. We analyze the transition to turbulence with the techniques of dynamical systems theory. The presence of an initial helical structure in the flow suggests that the chaotic dynamics has low dimensionality: the correlation dimension computed along the jet axis (18\ensuremath{\varphi}\ensuremath{\le}l\ensuremath{\le}24\ensuremath{\varphi}, where \ensuremath{\varphi} is the nozzle diameter) at R=543 shows that the dimension of the chaotic attractor increases continuously from \ensuremath{\sim}3 to \ensuremath{\sim}6. Good correlation is found between spatial coherence and attractor dimension, which confirms the validity of the values obtained for the chaotic attractor dimensionality. From local coherence measurements, we infer a power-law dependence between the attractor dimension and the local correlation length (the range of the local turbulent structure). This result clearly indicates that in open systems the attractor dimension (as computed from time series data) is to be connected to the local chaotic dynamics of the flow.