The active nature of vorticity is investigated in order to understand its difference with a passive scalar. The direct cascade down to small scales is examined through both classical and new diagnostics (based on tracer gradient properties) in numerical simulations of freely decaying two-dimensional (2D) turbulence. During the transient evolution of turbulence, the passive scalar possesses a stronger cascade due to different alignment properties with the equilibrium orientations obtained in the adiabatic approximation by Lapeyre et al. [Phys. Fluids 11, 3729 (1999)] and Klein et al. [Physica D 146, 246 (2000)]. In strain-dominated regions, the passive scalar gradient aligns better with the equilibrium orientation than the vorticity gradient does, while the opposite is true in effective-rotation-dominated regions. A study of the kinematic alignment properties shows that this is due to structures with closed streamlines in the latter regions. However, in the final evolutionary stage of turbulence, both active and passive tracer gradients have identical orientations (i.e., there is a perfect alignment between the two gradients, all the more so when they are stronger). The effect of diffusion on the cascade is also studied.

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