Chaotic Advection

When we say a dynamical system, or flow map, is chaotic we mean it is highly sensitive to initial conditions. This means that particles in the flow which may be close to each other initially (ie they represent similar initial conditions for the flow map) can be advected in very different ways. Chaotic advection is the advection of particles under a chaotic flow map or dynamical system. We care about this because chaotic mixing is efficient since particles initially close to each other separate exponentially. Note that at least 3 degrees of freedom is necessary to get a chaotic system, so steady 2 dimensional flows are not chaotic, but time-dependent 2 dimensional flows may be.