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If a hydrostatic fluid is compressible, the criterion for dynamic stability is not simply that denser fluid must lie below light fluid, but that small perturbations must tend to correct themselves.
When lower fluid is raised up into upper fluid, ( during which process the density of the lower fluid decreases due to the drop in pressure ), stability requires that it remain denser than the upper fluid, so that gravity pulls it back toward its original position.
The fluid is unstable if small perturbations tend to amplify themselves, i. e. if dense lower fluid, when displaced upward, expands enough to become lighter than the surrounding upper fluid, and therefore continues to move upward.

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