how to get the "Vorticity Transport Equation" by taking the curl of "compressible Navier-Stockes" equation?

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Brian G Higgins

The "answer" can be found on Wikipedia at http://en.wikipedia.org/wiki/Vorticity_equation

There you can see the key steps for deriving the vorticity transport equation, starting from the Navier-Stokes equations with variable density.

Lakshmi Sankar

See http://brennen.caltech.edu/fluidbook/basicfluiddynamics/equationsofmotion/vorticitytransport.pdf