Here's a fun little simulation I made in my fluid dynamics class taught by Gary Glatzmaier. In this simulation, the box is heated from below and cooled on top. I perturbed the system by changing the heating term on the bottom. During the first half of the simulation, the left side of the box was gradually heated while the right side was gradually cooled. This causes the temperature profile to "overturn" resulting in a hot upper layer and a cold bottom layer sandwiched between the top and bottom boundaries.