... as

The formal procedure of these steps and the construction of the associated variational principle is exemplified on a simple case in the Appendix.

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... criterion

The extension of the procedure to analyze the stability of the two dimensional problem is also straightforward.

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... fluctuation

The absence of the pressure term $-\partial_{z}p_{1}$ is related to the absence of an horizontal velocity component since in the incompressibility condition $\partial_{x}v_{x}+\partial_{z}v_{z}=0$ the first term is considered irrelevant.

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