Mixing with time dependent natural convection

Chaotic mixing inside a two dimensional cavity can be achieved with time dependent natural convection if the motion of a fluid is generated by imposing alternating hot and cold wall temperatures. With this set up no moving walls are required to mix the fluid inside the container. In this comment we illustrate this idea by numerically solving the governing equations of natural convection in a two dimensional square cavity with sections of its upper and lower horizontal walls cooled and heated in a periodic manner. These conditions generate a vortex of time dependent intensity that moves its center in a closed loop around the geometrical center of the container. The mixing properties of the flow are illustrated by Lagrangian tracking of a collection of points originally located in a line.