Can viscosity and forcing in a fluid flow result in chaotic advection?
” Abstract The Lagrangian (fluid particle) trajectories of a steady Euler flow in 2D are determined by an integrable system and hence exhibit no chaotic motion. The question then naturally arises as to whether a perturbed flow, which incorporates the physical effects of viscosity and forcing, can be chaotic. This problem is non-trivial since the perturbation is added at the level of the full partial differential equation but the potential chaos is at the level of the particle trajectories. It brings up many issues including long-time existence for 2D Navier-Stokes and finite-time Melnikov theory.
