Exact steady solutions of the inviscid incompressible flow equations can be constructed by superposing helical waves. Such flows have the Beltrami property that the vorticity vector is everywhere parallel to the velocity vector. Beltrami flows may have very complicated three-dimensional structures; in particular, fluid particle trajectories may be chaotic and space- filling. Chaotic particle motion is important in determining the effective eddy diffusivity of a flow, and its small-scale mixing properties. Chaos is also likely to influence concentration and coagulation in suspensions of particles whose densities are different from the fluid. The amplification of magnetic fields in electrically conducting fluids is yet another effect in which chaotic flow play a major role. The PIs will study the chaos in a number of Beltrami flows and explore its implications for these physical problems, how the chaotic properties depend on the complexity of the flow. The numerical work will be performed on a hypercube multiprocessor, which can follow the motion of a large number of particles simultaneously.
