Local and convected rates of change

[renlok]

Homework Statement

This is less of a help me answer something question more a help me understand this question.

I was reading though my hydrodynamics notes and there was a derivation that ended up with the follow equation
$$\frac{D\psi}{Dt} = \frac{\partial\psi}{\partial{t}} + (\underline{u}.grad)\psi$$
now i completely understood the derivation, what I don't understand is the result why doesn't $$\frac{D\psi}{Dt} = \frac{\partial\psi}{\partial{t}}$$? Also what do the capital D even mean?

Homework Equations

The Attempt at a Solution

 

[renlok]

no one?