Discussion
Which decomposition splits the velocity gradient into four parts?
Answer: B
The two by two horizontal velocity gradient tensor has exactly four independent components, conventionally taken as divergence, vertical vorticity and the two deformations. Every local distortion of a fluid element is a combination of these four. The vorticity equation terms describe how vorticity changes rather than how the flow is decomposed, and the Helmholtz split is a different and coarser division into two parts. Checking the units of each quantity catches a wrong formula before the arithmetic begins.
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