## Abstract

A two-dimensional approximation of the Navier-Stokes equations illustrates a specific instance of transition from Lagrangian to Eulerian turbulence. As the Reynolds number (Re) increases, the system describing the dynamics of the velocity field undergoes a transition from steady state to a limit cycle. At this point the flow displays chaotic advection-i.e., manifolds intersect transversely and Poincaré maps show the typical chaotic structure-but the velocity field itself is time-periodic and the power spectrum presents a fundamental frequency and its harmonics. As Re increases still further, the limit cycle bifurcates into a strange attractor producing a broadband power spectrum. The model suggests that Lagrangian turbulence (complex particle trajectories) might serve as a springboard for Eulerian turbulence (complex signal at a fixed point) and indicates a possible link between a kinematical view of flows and mixing and other viewpoints of turbulence based on strange attractors. The ideas can be generalized to three-dimensional flows; however, due to their simplicity, the flows generated are unable to mimic some key features of turbulence such as spatial uncorrelation of Eulerian signals.

Original language | English (US) |
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Pages (from-to) | 2024-2035 |

Number of pages | 12 |

Journal | Physics of Fluids A |

Volume | 2 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1990 |

## ASJC Scopus subject areas

- Engineering(all)