The equations in the "large fluid simulation" is wrong

General Discussion
1

https://doc.freefem.org/tutorials/aLargeFluidProblem.html
the navier-stokes is wrong, the correct form is
image
the divergence of the product of miu_{T} and the transpose of grad(u) is missing, it can’t be eliminated because miu_{T} is not constant

3

It is a well know simplication un case of Boussinesq approximation for the buoyancy, and the resultat are on golf agreement with experiment.

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