Lagrangian description of the vorticity cascade

In this section I will focus on the statistical properties of vorticity fluctuations $\delta_r \omega = \omega({\mbox{\boldmath$x$}}+{\mbox{\boldmath$r$}},t)- \omega({\mbox{\boldmath$x$}},t)$ at scales $r$ smaller than the correlation length $L$ of the external forcing. The intuitive arguments presented for the passive scalar will be reformulated in terms of Lagrangian description of the vorticity cascade, which allows to point out the crucial differences between the active and the passive problem.