Abstract
We consider a simple, nonlinear Hamiltonian model for particle motions in two-dimensional turbulence in which the stream function power spectrum has the form kγ (γ constant). We show that fluid particle trajectories, (1) while differentiable and chaotic at small scale, may be fractal space curves at larger scale, (2) undergo anomalous transport, and (3) have frequency spectra ∼fα in fully stochastic limit, where we obtain α=α(γ), a scaling law. Anomalous diffusion is shown to arise partly as a result of the fractal nature of the particle trajectories.