Structural stability in two-dimensional model flows: Lagrangian and Eulerian turbulence

T. J. Danielson*, J. M. Ottino

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageEnglish (US)
Pages (from-to)2024-2035
Number of pages12
JournalPhysics of Fluids A
Issue number11
StatePublished - 1990

ASJC Scopus subject areas

  • General Engineering


Dive into the research topics of 'Structural stability in two-dimensional model flows: Lagrangian and Eulerian turbulence'. Together they form a unique fingerprint.

Cite this