Active and passive scalars transported by an incompressible two-dimensional conductive fluid are investigated. It is shown that a passive scalar displays a direct cascade toward the small scales while the active magnetic potential builds up large-scale structures in an inverse cascade process. Correlations between scalar input and particle trajectories are found to be responsible for those dramatic differences as well as for the behavior of dissipative anomalies.

1. Description of the algorithm [postscript file, pdf file]
2. Fig.5
3. Fig.6
4. Fig.7
5. Fig.8
6. Movie [animated gif (2500Kb), mpeg (192Kb)]
   Animation of the backward evolution of the active scalar field (left) and
   of the particle propagator (right). Frames are equispaced by 1 eddy turnover time.
   Notice the strong correlation between the field and the propagator.
   

Fig.5: Probability densities of scalar fields normalized by their standard deviation:
active scalar (red curve), passive scalar (blue curve). The active scalar pdf is
indistiguishable from a Gaussian (dotted curve).
[postscript file]

Fig.6. Velocity spectrum E_v(k). Notice that at k < k _f the spectrum is shallower than k^-1.
[postscript file]

Fig.7. Probability densities of active scalar increments (red curve) and passive scalar
increments (blue curve) rescaled to their standard deviations, for three distances in the r=2 l_f, 4 l_f, 8 l_f.
[postscript file]

Fig.8. Compensated power spectrum of active scalar variance, E_a(k)k², at three different times of its evolution.
Notice the linear scale on the vertical axis.
[postscript file]