Explained: Substantial Derivative [Math]

The substantial (or total) derivative appears frequently when deriving the governing equations.  We can imagine that we hop on a fluid element as it is moving through a flow field, and we look at how the properties of the fluid element change.  This is fundamentally different than sitting still and watching the flow move through a fixed point, and then seeing how the properties change at that point.  This is why we have a local derivative term as well as a convective term.

Source:
Modern Compressible Flow with Historical Perspective, John D. Anderson

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