Abstract. The evolution of tracer "injected" into an equivalent barotropic eddy on the beta-plane is examined numerically. The eddy is governed by the standard quasigeostrophic equation, and the concentration of tracer is governed by the advection equation with diffusion. At the initial moment of time, the streamfunction and distribution of tracer are both radially or elliptically symmetric. After the first 10-30 days, a spirallike strip, where the gradient of concentration is large, develops in the tracer field, whereas the eddy remains smooth for a relatively long time. To put this conclusion in quantitative terms, a "tracer variability indicator" is introduced and shown to grow much faster than a similar characteristic of the potential vorticity field (notwithstanding the fact that the tracer concentration and PV satisfy the same governing equation). A simple explanation as to why the tracer is more affected by filamentation than PV is provided for eddies with small Burger number. It is demonstrated that the high-gradient strip develops, unless stopped by turbulent diffusion, into an inversion (non-monotonicity) of the tracer concentration field. Finally, the results of simulations are compared to the spiral patterns in the real-life eddies observed in the East Australian Current.