Power spectrum of passive scalars in two dimensional chaotic flows

In this paper the power spectrum of passive scalars transported in two dimensional chaotic fluid flows is studied theoretically. Using a wave-packet method introduced by Antonsen et al., several model flows are investigated, and the fact that the power spectrum has the k −1 -scaling predicted by Batchelor is confirmed. It is also observed that increased intermittency of the stretching tends to make the roll-off of the power spectrum at the high k end of the k −1 scaling range more gradual. These results are discussed in light of recent experiments where a k −1 scaling range was not observed.