Convection will be different depending on what kind of temperature gradient is present.
The system on the left is stable (i.e. does not move) because there is a decrease in temperature with x - a negative temperature gradient and thus a positive density gradient. This means that the density of the fluid increases with x and so gravity does not move the fluid. The fluid arranged in layers of equal density and temperature (density stratified). This is the condition which an unstable system “works towards”.
The system on the right is unstable due to the warmer fluid lying at the bottom, meaning that the less dense fluid is at the bottom - a positive temperature gradient and thus a negative density gradient. This density difference under gravity causes circulation of the fluid to move the more dense fluid to the bottom.
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