ELEMENTARY TOPOLOGY OF 2-DIMENSIONAL TURBULENCE FROM A LAGRANGIAN VIEWPOINT AND SINGLE-PARTICLE DISPERSION

We discuss a series of numerical experiments on the dispersion of neut rally buoyant particles in two-dimensional turbulent flows. The topolo gy of two-dimensional turbulence is parametrized in terms of the relat ive dominance of deformation or rotation; this leads to a segmentation of the turbulent field into hyperbolic and elliptic domains. We show that some of the characteristic structural domains of two-dimensional turbulent flows, namely coherent structures and circulation cells, gen erate particle traps and peculiar accelerations which induce several c omplex properties of the particle dispersion processes at intermediate times. In general, passive particles are progressively pushed from th e coherent structures and tend to concentrate in highly hyperbolic reg ions in the proximity of the isolines of zero vorticity. For large dis persion times, the background turbulent field is a privileged domain o f particle richness; there is however a permanent particle exchange be tween the background field and the energetic circulation cells which s urround the coherent structures. At intermediate times, an anomalous d ispersion regime may appear, depending upon the relative weight of the different topological domains active in two-dimensional turbulence. T he use of appropriate conditional averages allows the basic topology o f two-dimensional turbulence to be characterized from a Lagrangian poi nt of view. In particular, an intermediate t5/4 anomalous dispersion l aw is shown to be associated with the action of hyperbolic regions whe re deformation dominates rotation; the motion of the advected particle s in strongly elliptic regions where rotation dominates over deformati on is shown to be associated with a t5/3 dispersion law. Because neutr al particles concentrate on average in hyperbolic regions, the t5/4 di spersion law is quite robust and it can be observed under very general circumstances.