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Define the convective, total or material material derivative operator as

\frac{D}{Dt} = \frac{\partial}{\partial t} + \mathbf{U} \cdot \nabla

This relates the rate of change of a quantity within an infinitesimal control fluid volume that we would witness if we were riding with it along a streamline (Lagrangian viewpoint), to the rate of change of the quantity that a stationary observer would witness from their vantage point on the streamline (Eulerian viewpoint).