I have read this question and the accompanying answers - Linear Vs Non Linear Differential Equation as well as the useful comments and my question is related. I am in fluid dynamics and I deal with the material derivative on a daily basis and I recently read that the advective term
Here is the relevant text from the above link
"Note that the advection of momentum $(V · \nabla)V$ is non-linear and this is the term that leads to much of the interesting behaviour in fluid mechanics."
i.e $$ \mathbf u.\nabla A $$
where u is the flow velocity and A is any vector field is non linear and as a result the whole material derivative is non linear due to the presence of a single non linear term.
What exactly is the reason for the non linearity in the advective term of the material derivative ?
Is it because of the product of a tensor ( $ \nabla A$) and a vector ?