Abstract
This study pertains to the three-dimensional direct numerical simulation (DNS) of a vertically oscillating vessel containing an incompressible Newtonian liquid, surrounded by air at rest and ambient conditions. Squire's theorem was extended and shown to apply in this case, allowing for the theory of linear stability to be implemented and a comparison to be made with the DNS results. It was further discovered that the method by which a fluid instability is initiated in the numerical simulation affects the initial development of the instability. This phenomenon was confirmed through an optimal perturbations analysis. A possible physical explanation of this effect is also presented.
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