The dispersion of a passive tracer in a quasi‐two‐dimensional turbulent flow and the geometry of corresponding isoconcentration lines are investigated experimentally. The flow consists in an array of 900 vortices, forced in a thin layer and driven in a turbulent regime. Both the instantaneous velocity field and the concentration field are measured. A remarkable regime of anomalous diffusion—characterized by a dispersive front moving liket0.32±0.04—is observed. Examining the trajectories of individual neutral particles, we reveal the presence of ‘‘traps’’ that control most of the characteristics of this hypodiffusive regime. The fractal dimension of isoconcentration profiles and the exponents of the structure functions of both the velocity and the concentration fields are established. The corresponding values are consistent with mathematical inequalities, recently discovered, but show some disagreements with recent conjectured equalities proposed by Constantinetal. [Nonlinearity7, 1045 (1994)]. ©1996 American Institute of Physics.