VORTICITY GENERATION BY INSTABILITIES OF CHAOTIC FLUID-FLOWS

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.