Regular and chaotic motion of fluid particles in a two-dimensional fluid

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Abstract
The authors study the chaotic behaviour exhibited by particles which move in a two-dimensional fluid. The connection of this Lagrangian chaos with the velocity field behaviour is discussed both in the Lorenz model and in truncated Navier-Stokes equations. They indicate a possible method for the onset of Lagrangian chaos which seems to be rather generic. Lagrangian chaos appears when the Eulerian equation passes from a steady solution to a periodic one via Hopf bifurcation. It is also shown that the transition to chaos for the velocity field ('Eulerian chaos') does not affect the particle motion properties in some typical cases.