Dynamics of the orientation of active and passive scalars in two-dimensional turbulence

The active nature of vorticity is investigated in order to understand its d ifference with a passive scalar. The direct cascade down to small scales is examined through both classical and new diagnostics (based on tracer gradi ent 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 b y Lapeyre [Phys. Fluids 11, 3729 (1999)] and Klein [Physica D 146, 246 (200 0)]. In strain-dominated regions, the passive scalar gradient aligns better with the equilibrium orientation than the vorticity gradient does, while t he opposite is true in effective-rotation-dominated regions. A study of the kinematic alignment properties shows that this is due to structures with c losed streamlines in the latter regions. However, in the final evolutionary stage of turbulence, both active and passive tracer gradients have identic al orientations (i.e., there is a perfect alignment between the two gradien ts, all the more so when they are stronger). The effect of diffusion on the cascade is also studied. (C) 2001 American Institute of Physics.