We show that at high Reynolds number, smooth, Lagrangian chaotic flows
are typically linearly unstable and that the perturbed vorticity tend
s to concentrate on a fractal, Numerical integration of the relevant l
inear partial differential equations with Reynolds number up to R simi
lar to 10(6) shows that the wavenumber power spectrum of the perturbed
vorticity has a power-law behavior and that the magnitude of the pert
urbed vorticity is a multifractal. It is then shown that a wavepacket
picture, whereby vorticity wavepackets are evolved according to ordina
ry differential equations, yields scaling results and appropriately de
scribes the small wavelength features of bath the power spectrum and t
he multifractal dimension spectrum. Analytical results are derived est
ablishing the validity of the latter approach as well as an equivalenc
e principle for Lyapunov partition functions. These results are verifi
ed by numerical simulations involving a computationally efficient clas
s of chaotic flows.