I realize this may be an elementary question however I want to make sure I am not mistaken in my analysis.

I am uncertain what property of $\nabla$ means these two terms are not equal. (It came up in a fluid mechanics proof related to vorticity). (note: $u, v$ are vectors).

From continuity: $$ \nabla \cdot u = 0$$

Which means: $$ w( \nabla \cdot u)=0$$

However: $$ (u \cdot \nabla)w \neq 0 $$

Is it because the divergence will always act on the RH element first?

Any help is much appreciated


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.