Chaotic mixing
![An example of chaotic mixing](/Images/godic/202501/04/Chaotic_mixing1116.png")
![2-D Stationary flow: The velocity v is tangent to streamlines (dotted lines). For a stationary flow (left), Lagrangian trajectories X coincide with streamlines. For an unstationary flow (right), the position of streamlines changes with time and trajectories do no coincide with streamlines, hence better mixing is possible.](/Images/godic/202501/04/Streamline_stationary_2dflow1116.jpg")
![Blinking vortex flow: (a) The flow is created by the periodic alternated rotation of rods (b) The trajectory consists of arcs of circles. The particle can wander through the fluid domain (c) A small black disk of fluid is stretched into a large number that occupy the whole width of the fluid domain.](/Images/godic/202501/04/Blinking_vortex_flow1116.jpg")
![(a) In chaotic advection, neighboring trajectories separate exponentially fast with time. (b) Numerical integration of two trajectories initially very close, for a 2-D Stokes flow where a rod stirs fluid by moving on a figure-eight path. The trajectories separate fast because of chaotic advection, until they are completely uncorrelated.](/Images/godic/202501/04/Chaotic_advection_trajectories1116.png")
In chaos theory and fluid dynamics, chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow. The flow is characterized by an exponential growth of fluid filaments. Even very simple flows, such as the blinking vortex, or finitely resolved wind fields can generate exceptionally complex patterns from initially simple tracer fields.