It's quite confusing, the del operator means different things in each term. del of p is just the gradient of the pressure, but the convective term is more compl

It's quite confusing, the del operator means different things in each term. del of p is just the gradient of the pressure, but the convective term is more complicated. This may help [1]. The key part is: Generally the convective derivative of the field u•∇y, the one that contains the covariant derivative of the field, can be interpreted both as involving the streamline tensor derivative of the field u•(∇y), or as involving the streamline directional derivative of the field (u•∇) y, leading to the same result. [1] https://en.wikipedia.org/wiki/Material_derivative https://en.wikipedia.org/wiki/Material_derivative